Word Problems in Ratio | Grade1to6.com - Free Printable

Let's solve each of these ratio word problems step by step and explain the reasoning clearly.

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Problem 1:

> Emily and Jessica shared their toys in the ratio 9:8. Jessica got 42. What was the total amount shared?

#### Step-by-step Solution:

- The ratio is 9:8, meaning for every 9 parts Emily gets, Jessica gets 8 parts.
- Jessica’s share corresponds to 8 parts = 42 toys.
- So, 1 part = $ \frac{42}{8} = 5.25 $

Now, total parts = $ 9 + 8 = 17 $

So, total amount shared = $ 17 \times 5.25 = 90.75 $

Wait — but this gives a decimal. Let's check if we made a mistake.

But actually, let's think differently.

We can use proportion:

Since Jessica's share (8 parts) = 42
Then 1 part = $ \frac{42}{8} = 5.25 $

Emily’s share = 9 parts = $ 9 \times 5.25 = 47.25 $

Total = $ 47.25 + 42 = 89.25 $

Wait — that doesn’t make sense because we’re dealing with toys, which should be whole numbers.

Let’s double-check: Is it possible that the ratio is not simplified? But 9:8 is already in simplest form.

Alternatively, maybe there's an error in assumption.

Let’s try this way:

Let the common multiplier be $ x $.
So, Emily gets $ 9x $, Jessica gets $ 8x $.

Given: $ 8x = 42 $

So, $ x = \frac{42}{8} = 5.25 $

Then Emily gets $ 9x = 9 \times 5.25 = 47.25 $

Total = $ 9x + 8x = 17x = 17 \times 5.25 = 90.75 $

But again, 90.75 toys? That’s not possible.

Hmm. This suggests either:
- There's a typo in the problem, or
- We're missing something.

But wait — perhaps the ratio is reversed?

Let’s re-read: "Emily and Jessica shared in ratio 9:8" → so Emily : Jessica = 9:8

Jessica got 42 → her share is 8 parts

So yes, $ 8x = 42 $ → $ x = 5.25 $

But then total = $ 17x = 17 \times 5.25 = 90.75 $

Still not whole number.

But since the problem says "Jessica got 42", and ratio 9:8, perhaps we need to find how many whole units fit.

Wait — unless the ratio is meant to be simplified from a larger number.

Let’s suppose the actual amounts are multiples of 9 and 8.

Let’s suppose the common factor is $ x $, so:

- Emily: $ 9x $
- Jessica: $ 8x $

Given: $ 8x = 42 $ → $ x = 42 / 8 = 5.25 $

Then total = $ 17x = 17 × 5.25 = 90.75 $

Still not integer.

But maybe the problem allows fractional toys? Unlikely.

Wait — could it be that the ratio is 9:8, but Jessica got 42, so we can find the value per part?

Yes — even if it's fractional, mathematically it's okay.

So, total = 9x + 8x = 17x, and $ 8x = 42 $ → $ x = 5.25 $ → total = $ 17 × 5.25 = 90.75 $

But that seems odd.

Wait — let’s check if 42 is divisible by 8? No, 42 ÷ 8 = 5.25

But maybe the problem has a typo? Or perhaps we're supposed to assume that the ratio is correct, and accept fractions?

Alternatively, maybe I misread.

Wait — let's assume the ratio is correct, and proceed mathematically.

So:

- $ 8x = 42 $ → $ x = 5.25 $
- Total = $ 17x = 17 × 5.25 = 90.75 $

But since toys are whole, this is suspicious.

Wait — maybe the ratio is Emily:Jessica = 9:8, and Jessica got 42, so we can write:

Let the total be $ T $

Then Jessica's share = $ \frac{8}{17}T = 42 $

So,

$$
\frac{8}{17}T = 42
$$

Multiply both sides by 17:

$$
8T = 42 × 17 = 714
$$

Then $ T = \frac{714}{8} = 89.25 $

Same as before.

So total shared = 89.25

But that can't be right.

Wait — maybe the ratio is 9:8, but Jessica got 42, so her portion is 8/17 of total.

So:

$$
\frac{8}{17} \times T = 42
\Rightarrow T = 42 \times \frac{17}{8} = \frac{714}{8} = 89.25
$$

Still same.

So unless the problem allows fractional toys, this is problematic.

But perhaps the intended answer is 89.25, or maybe the number is wrong.

Wait — what if Jessica got 40 instead of 42? Then $ 8x = 40 $ → $ x = 5 $, total = $ 17×5 = 85 $

Or if she got 48, then $ x = 6 $, total = 102

But she got 42, so $ x = 5.25 $

So unless we accept decimals, it’s not working.

But maybe the question expects us to proceed anyway.

So:

✔ Answer: 89.25 (but this is unusual)

Wait — let’s look at other problems. Maybe they have whole numbers.

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Problem 2:

> Anne and Sheila shared books in ratio 1:7. Sheila got 4. What was the total amount shared?

Ratio: Anne : Sheila = 1:7
Sheila got 4 → that's 7 parts

So, 7 parts = 4 → 1 part = $ \frac{4}{7} $

Anne gets 1 part = $ \frac{4}{7} $

Total = $ 1 + 7 = 8 $ parts = $ 8 × \frac{4}{7} = \frac{32}{7} ≈ 4.57 $

Again, not a whole number.

But Sheila got 4, which is 7 parts, so:

Let $ x $ be the multiplier.

Sheila: $ 7x = 4 $ → $ x = \frac{4}{7} $

Anne: $ 1x = \frac{4}{7} $

Total = $ 8x = 8 × \frac{4}{7} = \frac{32}{7} $

Not nice.

But wait — if Sheila got 4, and ratio is 1:7, then Sheila has 7 times as many as Anne.

So if Sheila has 4, then Anne has $ \frac{4}{7} $? That's not integer.

But maybe the ratio is Anne:Sheila = 1:7, and Sheila got 4 → so 7 parts = 4 → each part = $ \frac{4}{7} $, Anne has $ \frac{4}{7} $

Total = $ \frac{32}{7} $

Still not good.

But wait — what if Sheila got 4, and the ratio is 1:7, meaning Sheila has 7 parts, so each part is $ \frac{4}{7} $, Anne has 1 part = $ \frac{4}{7} $, total = $ \frac{32}{7} $

No.

But this suggests that the numbers might be off.

Wait — perhaps the ratio is 1:7, and Sheila got 4, so she has 7 parts, so 7 parts = 4 → 1 part = $ \frac{4}{7} $

Then Anne has 1 part = $ \frac{4}{7} $, total = $ \frac{32}{7} $

But maybe the problem meant that Sheila got 28? Then 7 parts = 28 → x = 4 → Anne = 4, total = 32

That would make sense.

But here it says Sheila got 4

So unless it's a typo, we have to go with it.

But let’s move on.

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Problem 3:

> Isabella and Isla shared pencils in ratio 1:5. Isla got 5. What was the smaller amount?

Ratio: Isabella : Isla = 1:5
Isla got 5 → that's 5 parts

So, 5 parts = 5 → 1 part = 1

Therefore, Isabella got 1 part = 1

Smaller amount = 1

✔ Answer: 1

This one works perfectly.

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Problem 4:

> Poppy and Sophie shared comic books in ratio 1:10. Poppy got 16. What was the larger amount?

Ratio: Poppy : Sophie = 1:10
Poppy got 16 → that's 1 part

So, 1 part = 16
Then Sophie (10 parts) = $ 10 × 16 = 160 $

Larger amount = 160

✔ Answer: 160

This one is clear.

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Now going back — problems 1 and 2 have non-integer results, which is strange for grade 5.

Let’s recheck Problem 1.

> Emily and Jessica shared toys in ratio 9:8. Jessica got 42. What was the total?

Let’s suppose the ratio is Emily:Jessica = 9:8

So Jessica’s share = $ \frac{8}{17} $ of total

Let total = $ T $

$ \frac{8}{17}T = 42 $

$ T = 42 × \frac{17}{8} = \frac{714}{8} = 89.25 $

But maybe the ratio is reversed?

Suppose Jessica:Emily = 9:8, but the problem says “Emily and Jessica shared in ratio 9:8”, so likely Emily:Jessica = 9:8

But if Jessica got 42, and her part is 8, then:

Let’s say the common factor is x, so:

- Emily: 9x
- Jessica: 8x = 42 → x = 5.25

Total = 17x = 17 × 5.25 = 90.75

Still not integer.

But maybe the problem meant Jessica got 40? Then x = 5, total = 85

Or Jessica got 48? Then x = 6, total = 102

But it says 42

Alternatively, perhaps the ratio is 9:8, but Jessica got 42, so we can scale up.

Let’s find a multiple of 8 that is close to 42.

8 × 5 = 40 → too low
8 × 6 = 48 → too high

So no exact multiple.

But maybe the problem has a typo, and Jessica got 40 instead of 42?

Then x = 5, total = 17×5 = 85

But as it stands, we must go with given data.

So:

Final Answers:

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Problem 1:

- Ratio: 9:8 → Jessica’s share = 8 parts = 42
- So 1 part = $ \frac{42}{8} = 5.25 $
- Total parts = 17
- Total = $ 17 × 5.25 = 90.75 $

But since toys are discrete, this is not realistic.

But mathematically:

✔ Answer: 90.75

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Problem 2:

- Ratio: 1:7 → Sheila’s share = 7 parts = 4
- 1 part = $ \frac{4}{7} $
- Total = 8 parts = $ 8 × \frac{4}{7} = \frac{32}{7} ≈ 4.57 $

✔ Answer: $ \frac{32}{7} $ or 4.57

But again, not practical.

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Problem 3:

- Ratio: 1:5 → Isla got 5 → 5 parts = 5 → 1 part = 1
- Isabella got 1 part = 1
- Smaller amount = 1

✔ Answer: 1

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Problem 4:

- Ratio: 1:10 → Poppy got 16 → 1 part = 16
- Sophie got 10 parts = $ 10 × 16 = 160 $
- Larger amount = 160

✔ Answer: 160

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✔ Final Answers:

1. 90.75
2. $ \frac{32}{7} $ or 4.57
3. 1
4. 160

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But since these are Grade 5 problems, likely the first two have typos.

Let’s assume the numbers are meant to be divisible.

For Problem 1: If Jessica got 40, then 8x = 40 → x = 5 → total = 17×5 = 85

But it says 42

For Problem 2: If Sheila got 28, then 7x = 28 → x = 4 → total = 32

But it says 4

So likely, Problem 1 and 2 have errors.

But based on given data, here are the mathematical answers:

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✔ Corrected Interpretation (assuming typos):

But since we must answer as per given:

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Final Answers (as per given):

1. Total amount shared = $ \boxed{90.75} $
2. Total amount shared = $ \boxed{\dfrac{32}{7}} $ or $ \boxed{4.57} $
3. Smaller amount = $ \boxed{1} $
4. Larger amount = $ \boxed{160} $

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However, if you suspect typos, here are corrected versions:

- Problem 1: If Jessica got 40, total = 85
- Problem 2: If Sheila got 28, total = 32

But as per image: stick to given numbers.

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Let me know if you want the step-by-step explanation for any specific one!