Worksheet with two-step equations involving fractions and decimals, designed for math practice.

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, no explanatory or educational sections will be included. Only the final answer will be provided after verifying calculations.

Let’s solve each problem step by step:

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Problem 1:

Marion saved $209.06. She saves weekly allowance over 5 weeks.
So, weekly allowance = $209.06 ÷ 5 = $41.812 → round to nearest cent → $41.81

Check: 5 × $41.81 = $209.05 — close, but we need exact.

Actually, let’s do exact division:
209.06 ÷ 5 = 41.812 → which is $41.81 when rounded to nearest cent? But money usually keeps two decimals.

Wait — perhaps it's exact? Let’s check:
5 × 41.812 = 209.06 → yes, so her weekly allowance is $41.812, but since we can’t have fractions of a cent, maybe the problem expects us to keep it as is or round appropriately.

But in real life, allowances are in whole cents. So likely, the number is meant to be divided evenly.

Actually, 209.06 ÷ 5 = 41.812 → that’s not a whole cent. Hmm.

Wait — perhaps I misread. Let me re-read:

“Marion has saved up $209.06... over a five-week period”

So total saved = $209.06 over 5 weeks → weekly = 209.06 / 5 = 41.812 → which is $41.81 if rounded down, but that would make total $209.05.

Alternatively, maybe it’s $41.81 per week for 4 weeks and $41.82 for one week? But the problem doesn’t say that.

Actually, in math problems like this, we usually accept decimal answers even if they’re not whole cents, unless specified otherwise.

But let’s look at the other problems — they involve money with two decimals, so probably we should report to nearest cent.

209.06 ÷ 5 = 41.812 → rounds to $41.81

But let’s verify: 5 × 41.81 = 209.05 → off by 1 cent.

Perhaps it’s $41.812, and we leave it as is? But that’s not standard.

Wait — maybe I made a mistake. Let me calculate again:

209.06 ÷ 5:

5 × 41 = 205 → remainder 4.06
5 × 0.812 = 4.06 → yes, so 41.812

In currency, we might write it as $41.81, but technically it’s $41.812.

However, looking at the context, perhaps the problem expects us to use the exact value.

But let’s move on and come back.

Actually, let’s do all problems first.

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Problem 2:

Jonas spent $134.50 total for 3 children’s tickets.
Cost per child = 134.50 ÷ 3 = ?

Calculate: 134.50 ÷ 3

3 × 44 = 132 → remainder 2.50
3 × 0.833... = 2.50 → so 44.833...

So $44.833... → rounds to $44.83 per ticket? But let’s check: 3 × 44.83 = 134.49 → off by 1 cent.

Again, same issue.

134.50 ÷ 3 = 44.833... → which is $44.83 if rounded down, but total would be 134.49.

Perhaps the problem allows fractional cents? Unlikely.

Maybe I should keep it as fraction.

134.50 = 13450/100 = 269/2? Better to use decimals.

134.50 ÷ 3 = 44.8333... → so approximately $44.83, but to be precise, it’s $44.83 and 1/3 cent, which isn't practical.

In such cases, often the problem expects the exact decimal or rounded to nearest cent.

Let’s assume we round to nearest cent.

For problem 2: 134.50 ÷ 3 = 44.833... → rounds to $44.83

But 3 × 44.83 = 134.49, which is 1 cent less.

Perhaps it's $44.84? 3 × 44.84 = 134.52 — too much.

So best to report as $44.83 with note, but since it's a math problem, maybe they want the exact value.

I recall that in some curricula, they teach to keep extra digits during calculation and round at the end.

But here, it's straightforward division.

Let’s look at problem 3.

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Problem 3:

Girls are one-third of the class. 3 girls are absent. 4 girls attended.

So, total girls = 3 absent + 4 attended = 7 girls.

Girls are 1/3 of class, so total class = 7 × 3 = 21 students.

That’s clean. No rounding needed.

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Problem 4:

Monday collection: $99.55 from paid lunches.

Tuesday: 40 students ate, and collection was $19.00 more than Monday.

So Tuesday collection = 99.55 + 19.00 = $118.55

This was from 40 students, so cost per lunch = 118.55 ÷ 40

Calculate: 118.55 ÷ 40

40 × 2.96 = 118.40 → remainder 0.15
40 × 0.00375 = 0.15 → so 2.96375

So $2.96375 per lunch → rounds to $2.96 or $2.97?

Check: 40 × 2.96 = 118.40
40 × 2.97 = 118.80 — too big.

118.55 - 118.40 = 0.15, so 0.15 / 40 = 0.00375, so $2.96375

Typically, we round to nearest cent: 2.96375 → 2.96 (since 0.00375 < 0.005)

But let's see: 2.96375 is closer to 2.96 than 2.97? 2.96 is 2.96000, difference 0.00375; 2.97 is 2.97000, difference 0.00625 — so yes, closer to 2.96.

But in money, sometimes they round up, but standard is nearest.

However, 40 × 2.96375 = 118.55 exactly, so if we report $2.96, it's approximate.

But for the answer, probably $2.96 is expected.

Let's calculate exactly: 118.55 ÷ 40 = 11855/4000 = 2371/800 = 2.96375

So $2.96 when rounded to nearest cent.

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Problem 5:

Zoe worked 160 hours in July, entitled to $600.65.

She put in 5 hours overtime.

Paycheck received: $1030.45

We need to find how much she gets per hour of overtime.

First, find her regular hourly rate.

Regular pay for 160 hours = $600.65

So regular rate = 600.65 ÷ 160

Calculate: 600.65 ÷ 160

160 × 3.75 = 600 → remainder 0.65
160 × 0.0040625 = 0.65 → so 3.7540625

So approximately $3.754 per hour.

Now, total paycheck = $1030.45

This includes regular pay for 160 hours plus overtime pay for 5 hours.

Regular pay = $600.65

So overtime pay = total - regular = 1030.45 - 600.65 = $429.80

This is for 5 hours of overtime.

So overtime rate per hour = 429.80 ÷ 5 = $85.96

That seems high, but possible.

Check: 5 × 85.96 = 429.80 — yes.

And regular rate is about $3.75, so overtime is much higher, which makes sense if it's time-and-a-half or double, but here it's given as entitlement, so we don't need to assume.

The problem says "she is entitled to $600.65" for 160 hours, and she got $1030.45 including 5 hours overtime, so yes, overtime pay is 1030.45 - 600.65 = 429.80 for 5 hours, so per hour $85.96.

Now, back to problem 1.

Problem 1: Marion saved $209.06 over 5 weeks.

Weekly allowance = 209.06 ÷ 5 = 41.812

As discussed, this is $41.812 per week.

In money, we might report as $41.81, but let's see the context.

Perhaps the problem expects the exact value, but since it's money, likely to nearest cent.

But 41.812 is closer to 41.81 than 41.82? 41.81 is 41.810, difference 0.002; 41.82 is 41.820, difference 0.008 — so closer to 41.81.

But 5 × 41.81 = 209.05, which is 1 cent less than 209.06.

Similarly, 5 × 41.82 = 209.10, which is 4 cents more.

So neither is exact.

Perhaps it's $41.812, and we leave it, but that's not standard.

Another thought: maybe "saved up $209.06" includes interest or something, but the problem says "saves up her weekly allowance", so likely the allowance is constant.

Perhaps the 209.06 is exact, so weekly is 209.06 / 5 = 41.812, and for the answer, we can write $41.81, acknowledging the rounding.

But let's look at problem 2: 134.50 / 3 = 44.8333... which is $44.83 if rounded, but 3*44.83=134.49, off by 1 cent.

In many textbooks, they might expect the answer as a fraction or exact decimal.

For problem 2, 134.50 ÷ 3 = 13450/300 = 269/6 = 44 5/6 = 44.833... so $44.83 when rounded.

Similarly for others.

Perhaps for consistency, we'll round to nearest cent for all.

But for problem 3, it's exact: 21 students.

Problem 4: 118.55 / 40 = 2.96375 -> $2.96

Problem 5: 429.80 / 5 = 85.96 -> $85.96

For problem 1: 209.06 / 5 = 41.812 -> $41.81

For problem 2: 134.50 / 3 = 44.8333... -> $44.83

But let's confirm problem 2: if each ticket is $44.83, total for 3 is 134.49, but he spent 134.50, so perhaps it's $44.8333, and we report as $44.83.

Maybe the problem has a typo, but we have to go with what's given.

Another idea: in problem 2, "spent $134.50 on entry tickets for the adults" — wait, let's read carefully.

"Jonas, his wife and their 3 children made a trip... Jonas spent $134.50 on entry tickets for the adults."

Oh! I think I misread.

Let me read again:

"Jonas spent $134.50 on entry tickets for the adults."

But it says "for the adults", and there are Jonas and his wife, so 2 adults.

The sentence: "Jonas spent $134.50 on entry tickets for the adults."

And "if the adult tickets cost $23.50 for the entry tickets in total" — wait, no.

Let's read the full sentence:

"Jonas spent $134.50 on entry tickets for the adults. If the adult tickets cost $23.50 for the entry tickets in total, how much did the entry fee for each child cost?"

This is confusing.

Let me read carefully:

"2) Jonas, his wife and their 3 children made a trip to the Indiana state fair. Jonas spent $134.50 on entry tickets for the adults. If the adult tickets cost $23.50 for the entry tickets in total, how much did the entry fee for each child cost?"

This seems poorly worded.

"Jonas spent $134.50 on entry tickets for the adults." — so for adults only, he spent $134.50.

Then "If the adult tickets cost $23.50 for the entry tickets in total" — this is ambiguous.

Perhaps it's "if the adult tickets cost $23.50 each" or something.

Let me parse.

It says: "Jonas spent $134.50 on entry tickets for the adults." — so total for adults is $134.50.

Then "If the adult tickets cost $23.50 for the entry tickets in total" — this might mean that the cost per adult ticket is $23.50, but that doesn't make sense because 2 adults at $23.50 each would be $47, not $134.50.

Perhaps "cost $23.50" is a typo, and it's for children or something.

Another interpretation: perhaps "the adult tickets cost $23.50" means per ticket, but then total for adults should be 2 * 23.50 = 47, but he spent 134.50 on adults, which is inconsistent.

Unless "adults" includes more people, but it says Jonas and his wife, so 2 adults.

Perhaps "Jonas spent $134.50 on entry tickets for the adults" is incorrect, and it's for all tickets.

Let me read the sentence again: "Jonas spent $134.50 on entry tickets for the adults."

Then "If the adult tickets cost $23.50 for the entry tickets in total" — this is messy.

Perhaps "for the entry tickets in total" refers to something else.

Another possibility: "if the adult tickets cost $23.50 each" and "in total" is misplaced.

But 2 * 23.50 = 47, not 134.50.

Perhaps "Jonas spent $134.50" is for all tickets, not just adults.

Let me check the original text: "Jonas spent $134.50 on entry tickets for the adults."

But then it says "if the adult tickets cost $23.50 for the entry tickets in total" — this might mean that the total cost for adult tickets is $23.50, but that contradicts the $134.50.

I think there might be a typo in the problem.

Perhaps "Jonas spent $134.50" is the total for all tickets, and "for the adults" is a mistake.

Let me see the context.

"Jonas, his wife and their 3 children made a trip... Jonas spent $134.50 on entry tickets for the adults."

Then "If the adult tickets cost $23.50 for the entry tickets in total" — this is confusing.

Another interpretation: "if the adult tickets cost $23.50" means per ticket, and "for the entry tickets in total" is not part of it, but the sentence is "cost $23.50 for the entry tickets in total", which suggests total cost for adult tickets is $23.50.

But that can't be, because he spent $134.50 on adults.

Unless "adults" is a misnomer.

Perhaps "Jonas spent $134.50" is for the children's tickets or something.

Let's read carefully: "Jonas spent $134.50 on entry tickets for the adults." — so for adults, $134.50.

Then "If the adult tickets cost $23.50 for the entry tickets in total" — this might mean that the cost per adult ticket is $23.50, but then for 2 adults, it should be $47, not $134.50.

Unless there are more adults, but it says Jonas and his wife, so 2.

Perhaps "his wife" is not included, but that doesn't make sense.

Another idea: perhaps "Jonas spent $134.50" is the total amount he spent on all tickets, and "for the adults" is a error.

Let me assume that, because otherwise it doesn't make sense.

In many such problems, the total spent is for all tickets.

So let's assume that Jonas spent $134.50 on all entry tickets for 2 adults and 3 children.

Then, "if the adult tickets cost $23.50" — probably per ticket.

The sentence: "If the adult tickets cost $23.50 for the entry tickets in total" — perhaps "in total" is a mistake, and it's "each".

Because if adult tickets cost $23.50 each, then for 2 adults, 2*23.50 = $47.

Then the remaining for children's tickets = 134.50 - 47 = $87.50 for 3 children.

So per child = 87.50 / 3 = 29.1666... = $29.17

That makes sense.

If "cost $23.50 for the entry tickets in total" means total for adults is $23.50, then for 2 adults, $23.50 total, so per adult $11.75, but then he spent $134.50 on adults, which is inconsistent.

So likely, it's a typo, and it's "if the adult tickets cost $23.50 each".

I think that's the intended meaning.

So for problem 2: total spent $134.50 for 2 adults and 3 children.

Adult tickets: $23.50 each, so 2 * 23.50 = $47.00

Remaining for children: 134.50 - 47.00 = $87.50

Per child: 87.50 / 3 = 29.1666... = $29.17 (rounded to nearest cent)

Check: 3 * 29.17 = 87.51, which is 1 cent more than 87.50, so perhaps $29.16? 3*29.16=87.48, off by 2 cents.

87.50 / 3 = 29.1666... so $29.17 is standard rounding.

In some contexts, they might expect exact fraction, but for money, $29.17 is fine.

Now for problem 1, similarly, 209.06 / 5 = 41.812, which is $41.81 when rounded to nearest cent, even though 5*41.81=209.05, close enough, or perhaps the problem has 209.05, but it's written as 209.06.

Maybe it's $41.812, and we report as $41.81.

But let's see the answer format.

Perhaps for problem 1, since it's weekly allowance, and money, we can leave it as 41.812, but I think for consistency, we'll round to nearest cent.

Another thought: in problem 5, we have exact numbers, so for others, we can do the same.

For problem 1: 209.06 ÷ 5 = 41.812, so $41.81

For problem 2: with correction, $29.17

For problem 3: 21

For problem 4: 118.55 ÷ 40 = 2.96375 -> $2.96

For problem 5: 85.96

Now for problem 4, is it correct?

Monday: $99.55 from paid lunches.

Tuesday: 40 students ate, collection was $19.00 more than Monday, so 99.55 + 19.00 = 118.55

Cost per lunch = 118.55 / 40 = 2.96375 -> $2.96

But 40 * 2.96 = 118.40, which is 15 cents less, so perhaps it's $2.96, and the difference is due to rounding, or maybe they expect $2.96.

118.55 / 40 = 11855/4000 = 2371/800 = 2.96375, so to nearest cent, 2.96.

Some might argue to round up, but standard is nearest.

For problem 5, we have exact: overtime pay = 1030.45 - 600.65 = 429.80 for 5 hours, so 429.80 / 5 = 85.96, exact.

So no issue.

Now for problem 1, let's calculate exactly: 209.06 / 5 = 41.812, which is 41 and 812/1000 = 41 and 101.5/125, but in decimal, for money, it's common to report as $41.81.

Perhaps the problem intends for us to use the value as is.

But I think for the answer, we'll put $41.81.

Similarly for others.

So let's summarize:

1) $41.81

2) $29.17 (with the assumption that "adult tickets cost $23.50 each")

3) 21 students

4) $2.96

5) $85.96

Now for problem 2, to confirm, if adult tickets are $23.50 each, 2 adults = $47.00, total spent $134.50, so children's tickets = 134.50 - 47.00 = 87.50 for 3 children, so 87.50 / 3 = 29.1666... = $29.17

Yes.

If the problem meant something else, but I think this is logical.

So final answers:

1) 41.81

2) 29.17

3) 21

4) 2.96

5) 85.96

With units where appropriate.

Now for the response, since no options are true, only final answer.

But the instruction says "provide only the final correct answer" after reasoning, and since all options are false, we just provide the answers.

But typically, for multiple problems, we list them.

So I'll write the answers for each problem.

Final Answer:

1) $41.81
2) $29.17
3) 21 students
4) $2.96
5) $85.96

But to be precise, let's box them or something.

Since it's a single response, I'll list them.

In the final answer section, I can write:

For problem 1: $41.81
For problem 2: $29.17
For problem 3: 21
For problem 4: $2.96
For problem 5: $85.96

Yes.