Question

Buffalo Chicken Dip calls for ¾ cup of buffalo sauce and serves 12 people. If I am having 30 people over for a party, how much buffalo sauce will I need for my recipe?

Answer 1

`(15)/(8)` cup

This can also be expressed as the following:

`1(7)/(8)` cup

Explanation:

This problem involved ratios. A ratio is a way of expressing one value compared to another when the two values being compared are of a different unit. The problem gives one the general ratio of the following,

`sauce (cups) : people (number)`

Substitute in the given values, since one knows the units, it is unnecessary to write it,

`(3)/(4):12`

In this problem, the ratio of cups of sauce to people is constant, therefore one can say that the amount of sauce that (12) people need is proportional to the amount of sauce that (30) people need. Thus, set up an equation to solve for the unknown amount of sauce that (30) people need. Let parameter (x) represent the unknown amount of sauce.

`(3)/(4) : 12 = x : 30`

Use cross products to simplify,

`(12)(x)=((3)/(4))(30)`

Simplify,

`12x=(45)/(2)`

Inverse operations,

`12x = (45)/(2)`

Multiply both sides by (2)

`24x=45`

Divide both sides by (24),

`x=(45)/(24)`

Simplify,

`x=(15)/(8)`

Answer 2

15/8 cup or
`1(7)/(8)` cup

Explanation:

3/4 = 0.75

Ratios:

`(0.75)/(12) =(x)/(30) \\\\12x=22.5\\x= 15/8`