This worksheet challenges students with a variety of math operations, from calculating room areas to solving for 'x'.

It looks like you've uploaded a page from a math workbook or test, specifically Grade 4 problems, and it contains several multiple-choice questions. However, since I can't view images directly, I can’t see the actual image content — but based on your text input, I can help solve the visible problems.

Let’s go through each of the numbered problems listed (315–323) and solve them step by step. Here's the analysis:

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Problem 315

> John has 10 matches in a match of 6 bags. 7 matches in each of 3 bags and 7 matches in each of 10 bags. How many bags of 9 matches could he made using all of John’s matches?

Wait — this wording is confusing. Let's parse it carefully.

"John has 10 matches in a match of 6 bags." → This seems poorly worded.

Possibility: It might mean:
- He has 6 bags, each with 10 matches? Or
- "A match of 6 bags" — unclear.

But then it says:
"7 matches in each of 3 bags and 7 matches in each of 10 bags."

That suggests:
- 3 bags × 7 = 21 matches
- 10 bags × 7 = 70 matches

But earlier it said “10 matches in a match of 6 bags” — maybe that means 6 bags with 10 matches each?

So total matches:
- 6 × 10 = 60
- 3 × 7 = 21
- 10 × 7 = 70

Wait — that would be 60 + 21 + 70 = 151 matches?

But this doesn't make sense because the same bag can't be counted twice.

Alternatively, perhaps the sentence is:
> John has 10 matches in each of 6 bags, and 7 matches in each of 3 bags, and 7 matches in each of 10 bags?

But that would mean overlapping counts.

Alternatively, maybe it's a typo and meant to say:
> John has 10 matches in each of 6 bags, and 7 matches in each of 3 bags. Then how many bags of 9 matches can he make?

But even then, the numbers are inconsistent.

Wait — let's look at the next part:
“7 matches in each of 3 bags and 7 matches in each of 10 bags.” → That would be 3 + 10 = 13 bags with 7 matches each? But then what about the first part?

Perhaps the correct interpretation is:

> John has:
- 6 bags with 10 matches each → 6×10 = 60
- 3 bags with 7 matches each → 3×7 = 21
- 10 bags with 7 matches each → 10×7 = 70

But now we’re double-counting if these are all separate.

Unless it's saying:
- He has 6 bags with 10 matches each → 60
- And 3 bags with 7 matches → 21
- And 10 bags with 7 matches → 70

Total = 60 + 21 + 70 = 151 matches

Then how many bags of 9 matches can he make?

151 ÷ 9 = 16 full bags (16×9=144), remainder 7.

So answer: 16 bags

But this depends on interpretation.

Wait — perhaps it's a typo, and it should be:

> John has 6 bags with 10 matches each, and 3 bags with 7 matches each, and 10 bags with 7 matches each.

But that’s redundant.

Alternative interpretation: Maybe only two groups:
- 6 bags of 10 matches → 60
- 3 bags of 7 matches → 21
- Total = 81 matches

Then 81 ÷ 9 = 9 bags.

But the problem mentions "10 bags" again.

Wait — perhaps it's:
> John has 10 matches in each of 6 bags → 60
> and 7 matches in each of 3 bags → 21
> and 7 matches in each of 10 bags → 70

But that's impossible unless the 3 bags and 10 bags are separate.

Total matches = 60 + 21 + 70 = 151

151 ÷ 9 = 16.77... → 16 full bags of 9 matches.

Answer: 16

But let's check the options later.

Wait — perhaps it's a misprint and should be:

> John has 6 bags with 10 matches each, and 3 bags with 7 matches each. How many bags of 9 matches can he make?

Then total = 6×10 + 3×7 = 60 + 21 = 81

81 ÷ 9 = 9

Answer: 9

But the problem says “10 bags” — so maybe not.

Alternatively, maybe it's:

> John has 6 bags with 10 matches each → 60
> and 10 bags with 7 matches each → 70
> total = 130

130 ÷ 9 = 14.44 → 14 bags

Still not clear.

Wait — perhaps the sentence is:
> John has 10 matches in a match of 6 bags → probably means 6 bags × 10 = 60
> and 7 matches in each of 3 bags → 21
> and 7 matches in each of 10 bags → 70

But that's three sets.

Unless it's saying:
- 6 bags with 10 matches → 60
- 3 bags with 7 matches → 21
- 10 bags with 7 matches → 70

Total = 60+21+70 = 151

151 ÷ 9 = 16 full bags (144), remainder 7 → 16

But maybe the 3 bags and 10 bags are the same? Unlikely.

Alternatively, maybe it's:
> John has 10 matches in each of 6 bags → 60
> and 7 matches in each of 10 bags → 70
> total = 130

Then 130 ÷ 9 = 14.44 → 14 bags

But then where does the 3 bags come in?

This is ambiguous.

Wait — perhaps the original says:
> John has 10 matches in each of 6 bags, and 7 matches in each of 3 bags. How many bags of 9 matches can he make?

Then:
6×10 = 60
3×7 = 21
Total = 81
81 ÷ 9 = 9

Answer: 9

And option (B) is 9.

So likely the problem was miswritten.

Let me assume the intended meaning is:
> John has 6 bags with 10 matches each and 3 bags with 7 matches each.

Total matches = 6×10 + 3×7 = 60 + 21 = 81

How many bags of 9 matches can he make?

81 ÷ 9 = 9

✔ Answer: (B) 9

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Problem 316

> Jorga wants a shoe gift coupon. The shoes she likes cost $60. She has saved $30. She earns $10 per week. How many weeks will it take her to save enough?

She needs: $60 - $30 = $30 more

Earnings: $10 per week

Weeks needed: $30 ÷ $10 = 3 weeks

Answer: (C) 3

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Problem 317

> What % of pictures of pets that can paint a large room? To paint a large room, the worker used ___ gallons of paint.

This is incomplete. There's no data given.

But looking at the context, it may be a typo or missing diagram.

But then it says: “To paint a large room, the worker used ___ gallons of paint.”

And then it gives options: (A) 15.6, (B) 15.67, (C) 11.6, (D) 9.2, (E) 10.2

But no information on how much paint was used.

Wait — maybe there's a diagram or chart missing.

But in the text, it says:
> A triangle has sides 12", 13", 15". Area = ?

Wait — no, that's Problem 318.

Let’s skip and come back.

Wait — maybe Problem 317 is about percentages of pet pictures, but no data.

Possibly a typo.

But then it says: “To paint a large room, the worker used ___ gallons of paint.”

Maybe it's referring to a previous problem or diagram.

Since we don’t have the diagram, we can’t solve it.

But perhaps it's a separate question.

Wait — maybe it's asking: “What percentage of pictures of pets can paint a large room?” — which doesn't make sense.

Likely a misprint.

Perhaps it's supposed to be:

> A worker used 15.6 gallons of paint to paint a large room. What is the amount?

But then why ask for percentage?

Alternatively, maybe it's about area and paint coverage.

But without data, we can't solve.

Let’s move to Problem 318.

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Problem 318

> A triangle has sides 12", 13", 15". What is its area?

We can use Heron’s formula.

Sides: a = 12, b = 13, c = 15

Semi-perimeter: s = (12 + 13 + 15)/2 = 40/2 = 20

Area = √[s(s-a)(s-b)(s-c)]
= √[20(20-12)(20-13)(20-15)]
= √[20 × 8 × 7 × 5]
= √[20 × 8 × 7 × 5]

Calculate:
20 × 8 = 160
7 × 5 = 35
160 × 35 = 5600

√5600 ≈ ?

We know:
74² = 5476
75² = 5625

So √5600 ≈ 74.8

But let's compute exactly:

5600 = 100 × 56 → √5600 = 10√56 = 10×√(4×14) = 10×2√14 = 20√14

But numerically: √5600 ≈ 74.83

But options are:
(A) 72", (B) 74", (C) 76", (D) 78", (E) 80"

Wait — units are in inches? But area is in square inches.

But the answer choices are just numbers — probably area in sq.in.

74.83 is closest to 75, but 75 isn't an option.

Options: 72, 74, 76, 78, 80

74.83 is closer to 75, but not listed.

Wait — did I miscalculate?

Check: 20 × 8 × 7 × 5

20 × 8 = 160
7 × 5 = 35
160 × 35 = ?

160 × 35 = 160 × (30 + 5) = 4800 + 800 = 5600 ✔

√5600 = ?

Try 74.8² = ?

74² = 5476
75² = 5625
Difference: 5625 - 5600 = 25

So √5600 ≈ 75 - (25)/(2×75) = 75 - 25/150 = 75 - 1/6 ≈ 74.83

Yes.

But 74.83 is not among options.

Wait — maybe the triangle is right-angled?

Check: 12² = 144, 13² = 169, 15² = 225

Is 12² + 13² = 144 + 169 = 313 ≠ 225

12² + 15² = 144 + 225 = 369 ≠ 169

13² + 15² = 169 + 225 = 394 ≠ 144

Not right triangle.

Wait — maybe I misread.

Wait — perhaps it's a typo.

Alternatively, use coordinates.

Or maybe use another method.

Wait — perhaps the answer is 72?

Let’s try another way.

Use formula: Area = (1/2)ab sin C

But we don’t know angles.

Alternatively, use coordinates.

Place triangle with sides 12, 13, 15.

Assume base = 15, height h.

Then area = (1/2)×15×h

We can find height using Pythagoras.

Split base into x and 15-x

Then:
x² + h² = 12² = 144
(15-x)² + h² = 13² = 169

Subtract equations:

(15-x)² + h² - (x² + h²) = 169 - 144 = 25

(225 - 30x + x²) - x² = 25
225 - 30x = 25
30x = 200
x = 20/3 ≈ 6.666...

Then h² = 144 - x² = 144 - (400/9) = (1296 - 400)/9 = 896/9

h = √(896/9) = √896 / 3

√896 = √(64×14) = 8√14 ≈ 8×3.7417 = 29.9336

Then h ≈ 29.9336 / 3 ≈ 9.9778

Then area = (1/2) × 15 × 9.9778 ≈ 7.5 × 9.9778 ≈ 74.83

Same as before.

So area ≈ 74.83 → closest to 75, but options are 72, 74, 76, 78, 80

So 74 is closest.

But 74.83 is closer to 75, but not listed.

Wait — maybe I made a mistake.

Wait — perhaps the triangle is 12, 13, 15 — but is it possible?

Wait — 12 + 13 > 15 → 25 > 15 → yes

But area is ~74.8

So (B) 74" is the best choice.

But unit is "inches"? No — area should be sq.in.

But answer choices are just numbers — likely they expect 74.

So answer: (B) 74

But let’s check if any other method gives exact value.

Wait — perhaps it's a known triangle.

Alternatively, maybe the answer is 72?

No — calculation shows ~74.8

So likely (B) 74

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Problem 319

> The number 9 and 10 are the two smallest consecutive numbers which numbers such that the larger (10) is divisible by 2 and the smaller (9) is divisible by 3.

Find the two smallest consecutive numbers such that the larger is divisible by 7 and the smaller by 5.

So:
- n and n+1
- n+1 divisible by 7 → n+1 ≡ 0 mod 7 → n ≡ 6 mod 7
- n divisible by 5 → n ≡ 0 mod 5

So solve:
n ≡ 0 mod 5
n ≡ 6 mod 7

Find smallest n satisfying both.

List multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...

Check which ≡ 6 mod 7:

5 mod 7 = 5
10 mod 7 = 3
15 mod 7 = 1
20 mod 7 = 6 → yes!

So n = 20

Then n+1 = 21

Check:
- 20 divisible by 5 → yes
- 21 divisible by 7 → yes

Are they consecutive? Yes.

So the two numbers are 20 and 21

Sum = 20 + 21 = 41

Answer: (C) 41

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Problem 320

> A barrel full of apples weighs 42 pounds. The same barrel full of sand weighs 72 pounds. The sand weighs 2 times as much as the apples. What does the empty barrel weigh?

Let:
- Weight of apples = A
- Weight of sand = S
- Weight of barrel = B

Given:
- A + B = 42
- S + B = 72
- S = 2A

Now substitute:

From S = 2A, plug into second equation:

2A + B = 72

But A + B = 42 → B = 42 - A

Plug into above:

2A + (42 - A) = 72
2A + 42 - A = 72
A + 42 = 72
A = 30

Then B = 42 - 30 = 12

So barrel weighs 12 pounds

Answer: (A) 12 lbs

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Problem 321

> If 0.2 = 1/5 and 7.15 = 1.1, then what is 0.4?

Wait — this is strange.

0.2 = 1/5 → true

7.15 = 1.1 → false? 7.15 ≠ 1.1

Unless it's a code or pattern.

Wait — maybe it's a typo.

Perhaps it's: If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But 7.15 = 1.1 doesn’t make sense.

Unless it's a function or transformation.

Wait — maybe it's a digit replacement?

Or perhaps it's a ratio?

Alternatively, maybe it's: 0.2 corresponds to 1/5, and 7.15 corresponds to 1.1, but that’s inconsistent.

Wait — perhaps it's a typo and meant to be:

If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But still, 7.15 = 1.1 is not true.

Wait — maybe it's about decimal places?

Another idea: Perhaps it's a pattern where digits are shifted.

Alternatively, maybe it's a misprint.

Wait — perhaps it's:

> If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But 7.15 = 1.1 is false.

Unless it's a different system.

Wait — perhaps it's: 7.15 means 7 + 1.5 = 8.5, but 1.1 is not related.

Alternatively, maybe it's a cipher.

But this seems broken.

Wait — perhaps it's:

> If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But 0.2 = 1/5 → true

7.15 = 1.1 → false

Unless it's a typo and meant to be: 7.15 = 7.15, and 1.1 is something else.

Wait — maybe it's: If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But still.

Alternatively, perhaps it's: 0.2 corresponds to 1/5, and 7.15 corresponds to 1.1, so what is 0.4?

But no relation.

Wait — maybe it's a proportion.

But no.

Perhaps it's a misprint and should be:

> If 0.2 = 1/5, and 0.4 = ?, then what is 0.4?

But that’s trivial.

Wait — maybe the problem is:

> If 0.2 = 1/5, and 7.15 = 1.1, then what is 0.4?

But 7.15 = 1.1 is nonsense.

Alternatively, maybe it's a typo and meant to be:

> If 0.2 = 1/5, and 0.4 = 2/5, then what is 0.4?

But that’s too simple.

Wait — perhaps it's about rounding?

0.2 = 1/5 = 0.2

7.15 rounded to one decimal is 7.2, not 1.1

No.

Wait — maybe it's a fraction conversion:

0.2 = 1/5

7.15 = 715/100 = 143/20 = 7.15

1.1 = 11/10

No relation.

This problem seems corrupted.

But then it says: “then what is 0.4?”

But 0.4 = 2/5

So answer: (A) 2/5

But the options are:
(A) 2/5
(B) 1/4
(C) 1/3
(D) 2/3
(E) 3/4

So likely the intended answer is (A) 2/5

Even though the middle part is garbled.

So assume: If 0.2 = 1/5, then 0.4 = 2/5

Answer: (A) 2/5

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Problem 322

> Debra has only nickels and dimes. She has 12 coins totaling $1.20.

Let:
- n = number of nickels (5¢)
- d = number of dimes (10¢)

Equations:
n + d = 12
5n + 10d = 120 (since $1.20 = 120¢)

Multiply first equation by 5:
5n + 5d = 60

Subtract from second:
(5n + 10d) - (5n + 5d) = 120 - 60
5d = 60 → d = 12

Then n = 0

So she has 12 dimes, 0 nickels.

But then how many nickels? 0

Answer: (A) 0

But let’s check:
12 dimes = 12 × 10 = 120¢ = $1.20 → yes

So she has 0 nickels

Answer: (A) 0

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Problem 323

> Two cars start from the same point and drive in opposite directions. Car A travels at 40 mph, car B at 60 mph. After 2 hours, how far apart are they?

Relative speed = 40 + 60 = 100 mph

Time = 2 hours

Distance = 100 × 2 = 200 miles

Answer: (D) 200 miles

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## Final Answers:

| Problem | Answer |
|--------|--------|
| 315 | (B) 9 |
| 316 | (C) 3 |
| 317 | Incomplete — cannot solve |
| 318 | (B) 74 |
| 319 | (C) 41 |
| 320 | (A) 12 lbs |
| 321 | (A) 2/5 |
| 322 | (A) 0 |
| 323 | (D) 200 |

Note: Problem 317 lacks sufficient information. Please provide the diagram or clarify the context.

Let me know if you'd like explanations for any specific problem!