Question

A baker mixes 1 3/4 pounds of sugar for every 7/8 pound of butter to begin making frosting. The baker uses 168 pounds of butter and sugar to start the frosting. How much sugar does the baker use?


the options are:

1. 58 pounds

2. 84 pounds

3. 112

Answer 1

Answer:

3) 112

Step-by-step explanation:

Given:

Sugar used = 1¾ pounds

Butter used = $\frac{7}{8}$

Let sugar and butter be denoted as A and B.

This means the ratio of sugar to butter is A:B

Also, A+B = 168 Pounds

Let's first simplify 1¾ by multiplying 4 by 1,then add 3. We now have amount of sugar as $\frac{7}{4}$.

Therefore,

$A:B = \frac{7}{4} : \frac{7}{8}$

Dividing them, we have:

$\frac{A}{B} = \frac{\frac{7}{4}}{\frac{7}{8}}$

$\frac{A}{B} = \frac{7}{4} * \frac{8}{7}$

Solving further, we have:

$\frac{A}{B} = 2$

$A= 2B$

We already know A+B = 168

Let's substitute 2B for A

We have:

2B + B = 168

3B = 168

B = 56

To find A, lets substitute 56 for B,

We have:

A + B = 168

A + 56 = 168

A = 168 - 56

A = 112

Therefore, the baker uses 112 pounds of sugar

Answer 2

Answer:

The baker uses 112 pounds of sugar

Step-by-step explanation:

The baker mixes 1 3/4 pounds of sugar for every 7/8 pounds of butter to begin frosting. The baker uses 168 pounds of butter and sugar to start the frosting .

1 3/4 = 7/4 pounds of sugar for every 7/8 pounds of butter. It can be express in ratio as

7/4 of sugar  : 7/8 of butter

The amount of sugar the baker uses can be solved using the proportion below,

amount of sugar = a

amount of butter plus sugar = 168

Therefore,

7/4 + 7/8 = (14 + 7)/8 = 21/8(total used)

7/4 ÷ 21/8 = a/168

7/4 × 8/21 = a/168

8/12 = a/168

cross multiply

12a = 1344

a = 1344/12

a = 112  pounds

The baker uses 112 pounds of sugar