Math  /  Numbers & Operations

QuestionIf there are 90 calories in 34\frac{3}{4} cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270 calories 360 calories

Studdy Solution

STEP 1

What is this asking? If a little bit of yogurt has some calories, how many calories does more yogurt have? Watch out! Don't mix up the fractions and multiply incorrectly!

STEP 2

1. Calories per cup
2. Total Calories

STEP 3

Alright, so we're given that 34\frac{3}{4} of a cup of yogurt has 9090 calories.
Let's figure out how many calories are in just **one** cup!

STEP 4

We can set up a proportion: 90 calories34 cup=x calories1 cup\frac{90 \text{ calories}}{\frac{3}{4} \text{ cup}} = \frac{x \text{ calories}}{1 \text{ cup}}.
See how we've got calories on top and cups on the bottom on both sides?
Gotta keep those units consistent!

STEP 5

To solve for xx, we can multiply both sides of the equation by 11 cup.
This gives us x=9034x = \frac{90}{\frac{3}{4}}.

STEP 6

Dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of 34\frac{3}{4} is 43\frac{4}{3}, so we have x=9043x = 90 \cdot \frac{4}{3}.

STEP 7

Now, we multiply! 9043=9043=3603=12090 \cdot \frac{4}{3} = \frac{90 \cdot 4}{3} = \frac{360}{3} = 120.
So there are **120 calories** in **one cup** of yogurt!

STEP 8

We know there are 120120 calories in one cup, and we want to know how many calories are in **3** cups.

STEP 9

We simply multiply the calories per cup by the number of cups: 120 calories/cup3 cups=360 calories120 \text{ calories/cup} \cdot 3 \text{ cups} = 360 \text{ calories}.

STEP 10

There are **360 calories** in 3 cups of yogurt.

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