Amelia is making a cookie recipe that requires 4 cups of sugar for every 12 cups of flour. Amelia only has 9 cups of flour. She concludes that she will only need 3 cups of sugar Is Amelia correct? Why or why not? A Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12.

B Amelia is correct. One-quarter the amount of sugar is needed because only one-quarter of the recipe will be made.

C Amelia is incorrect. The number of cups of sugar must be reduced by 3 because the number of cups of flour is reduced by 3.

D Amelia is incorrect. She needs 4 cups of sugar because decreasing the number of cups of flour by 3 requires increasing the number of cups of sugar by 3.

Choice A)

Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12

Explanation:

It might help to think of the ratio 4:12 as the fraction 4/12. Dividing both parts by 4 leads to 1/3.

Similarly, the ratio 3:9 becomes 3/9 which reduces to 1/3.

This shows that 4/12 = 3/9, so the ratios 4:12 and 3:9 are the same.

Another way to show two fractions are equal is to do the steps below

4/12 = 3/9

4*9 = 12*3 ... cross multiply

36 = 36

Since the last equation is true, the first equation must be true.

Here's another way to see Amelia is correct.

So we know that 4 cups of sugar go with 12 cups of flour. This forms the fraction 4/12.

We also know that she has 9 cups of flour. Let's say we don't know how much sugar she needs, so we'll call this x. We have x cups of sugar go with 9 cups of flour. This forms the fraction x/9.

Equate the two fractions and solve for x

4/12 = x/9

9*4 = 12*x ... cross multiply

36 = 12x

12x = 36

x = 36/12 ... divide both sides by 12

x = 3

She needs 3 cups of sugar

The steps in this section are very similar to the steps in the last section.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3