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

The baker uses 112 pounds of sugar

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

Answer 2

3) 112

Explanation:

Given:

Sugar used = 1¾ pounds

Butter used =
`(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
`(7)/(4)`.

Therefore,

`A:B = (7)/(4) : (7)/(8)`

Dividing them, we have:

`(A)/(B) = ((7)/(4))/((7)/(8))`

`(A)/(B) = (7)/(4) * (8)/(7)`

Solving further, we have:

`(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