Question

Claire loves to drink smoothies for breakfast. Usually, she mixes 2 2/3 cups of frozen fruit, ½ cup of peanut butter, 1 3/4 cups of juice, and 1 ¼ cup of yogurt. She makes enough for herself and her husband.

If she has 6 cups of yogurt, how much
peanut butter will she need?

Answer 1

To determine how much peanut butter Claire will need, we first need to establish the ratio of peanut butter to yogurt in her smoothie recipe.

According to the recipe, for 1 ¼ cups of yogurt, Claire uses ½ cup of peanut butter. Therefore, the ratio of peanut butter to yogurt is:

Peanut butter : Yogurt = 1/2 : 1 1/4

To find out how much peanut butter Claire will need when she has 6 cups of yogurt, we can set up a proportion:

(1/2) / (1 1/4) = x / 6

To simplify the proportion, we convert the mixed fraction 1 1/4 to an improper fraction:

(1/2) / (5/4) = x / 6

Next, we can multiply the numerator of the left fraction by the reciprocal of the denominator:

(1/2) * (4/5) = x / 6

Simplifying the left side of the equation:

2/2 * 4/5 = x / 6

4/5 = x / 6

Now we can solve for x by cross-multiplying:

4 * 6 = 5x

24 = 5x

Dividing both sides of the equation by 5:

24/5 = x

The result is x = 4.8.

Therefore, Claire will need approximately 4.8 cups of peanut butter when she has 6 cups of yogurt.