Multistep Ratio and Percent Word Problems - Step-by-Step Lesson ... - Free Printable

Let’s solve each problem step by step.

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Problem 1: Andrea and the recipe

Andrea needs 3 cups of milk for every 2 cups of cream.
She used 8 cups of milk. We need to find how many teaspoons of cream she used.

But wait — the explanation in the worksheet says:

> For every 2 cups of milk, teaspoons of cream required = 1/2
> For every 1 cup of milk, teaspoons of cream required = (1/2) × (1/2) = 1/4? Wait — that doesn’t match.

Actually, let’s read carefully from the worksheet’s own explanation:

It says:
- For every 2 cups of milk, you need 1/2 teaspoon of cream? That seems odd — but let’s follow their logic as written.

Wait — looking again at the worksheet text:

> “For every 2 cups of milk, teaspoons of cream required = 1/2” → So ratio is:
Milk : Cream = 2 cups : 0.5 tsp

Then it says:
> “For every 1 cup of milk, teaspoons of cream required = 1/2 × 1/2 = 1/4”? No — actually, they wrote:

> “For every 1 cup of milk, teaspoons of cream required = 1/2 × 1/2” — that must be a typo or miswriting.

Actually, re-reading:

They say:
> “For every 2 cups of milk, teaspoons of cream required = 1/2”
→ So per 1 cup of milk: (1/2) ÷ 2 = 1/4 teaspoon

Then for 8 cups of milk:
8 × (1/4) = 2 teaspoons

And then they write:
> “So the number of teaspoons of cream are needed = 2”

✔ So Problem 1 answer is 2 teaspoons.

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Problem 2: Gas prices increasing by 115%

Current price per gallon = $2.50
Increase = 115% of current price

First, calculate 115% of $2.50:

115% = 115/100 = 1.15
So increase amount = 1.15 × 2.50

Let’s compute that:

1.15 × 2.50
= (1 × 2.50) + (0.15 × 2.50)
= 2.50 + 0.375
= 2.875

So the price increases by $2.875

New projected price = original + increase
= 2.50 + 2.875 = $5.375

The worksheet rounds this to $5.37 — probably because money is usually rounded to nearest cent.

$5.375 → round to nearest cent → look at third decimal: 5 → round up → $5.38?

Wait — hold on! The worksheet says:

> “So the projected cost of a gallon of gas for the end of next year is $5.37.”

But 2.50 + 2.875 = 5.375 → which should round to $5.38, not $5.37.

Did they make a mistake?

Let me check their calculation:

They wrote:
> $2.50 + 2.50 × (115%) = 2.50 + 2.50 × 1.15 = 2.50 + 2.875 = 5.375 → then they wrote $5.37

That’s incorrect rounding. 5.375 rounded to two decimals is 5.38, because the digit after hundredths is 5 → we round up.

BUT — maybe they meant something else?

Wait — perhaps they interpreted “increase by 115%” differently?

No — standard interpretation: if something increases by 115%, you add 115% of the original to itself.

Alternatively, sometimes people confuse “increased to 115%” vs “increased by 115%”.

If it increased to 115%, then new price = 1.15 × 2.50 = 2.875 — but that would mean decreased? No, 115% of original is more than original.

Wait — no: “increased by 115%” means you take original and ADD 115% of it.

So yes: 2.50 + (1.15 × 2.50) = 2.50 × (1 + 1.15) = 2.50 × 2.15

Oh! Maybe that’s easier:

Total multiplier = 1 + 1.15 = 2.15
So new price = 2.50 × 2.15

Calculate that:

2.50 × 2.15
= 2.50 × (2 + 0.15)
= (2.50 × 2) + (2.50 × 0.15)
= 5.00 + 0.375
= 5.375

Same result.

Now, rounding 5.375 to nearest cent:

Look at thousandths place: 5 → so round up the hundredths place (7 becomes 8)

→ $5.38

But the worksheet says $5.37 — that’s likely an error in the worksheet.

However, since the user uploaded the worksheet and it shows $5.37 as the answer, and our job is to solve accurately — we must go with correct math.

Unless... did they mean “increase of 15%”? But no, it clearly says 115%.

Another possibility: maybe “115%” was a typo and they meant 15%? Let’s test:

If increase by 15%:
2.50 × 1.15 = 2.875 → still same number, but that would be total price, not increase.

Wait — no: if increase by 15%, then new price = 2.50 × 1.15 = 2.875 ≈ $2.88 — but that’s not what the worksheet got.

Worksheet got 5.37 — which matches 2.50 × 2.15 = 5.375 → rounded down incorrectly to 5.37.

In real-world money, we always round 0.005 up — so 5.375 → 5.38.

Therefore, accurate answer is $5.38

But let’s double-check with exact fractions:

2.50 = 5/2
115% = 23/20
Increase = (5/2) × (23/20) = 115 / 40 = 23/8 = 2.875
Total = 5/2 + 23/8 = 20/8 + 23/8 = 43/8 = 5.375 → definitely 5.375

Rounded to cents: $5.38

So I will go with $5.38 as the correct answer, even though the worksheet says $5.37 — because we’re solving accurately.

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Final Answers:

Problem 1: 2 teaspoons
Problem 2: $5.38

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Final Answer:
Problem 1: 2
Problem 2: 5.38