Question

One gram of protein contains 4 calories. One gram of fat contains 9 calories. A snack has 60 calories from p grams of protein and f grams of fat The equation 4p + 9f = 60 represents the relationship between these quantities. 1. Determine if each pair of values could be the number of grams of protein and fat in the snack. Be prepared to explain your reasoning. b. 10.5 grams of protein and 2 grams of fat c. 8 grams of protein and 4 grams of fat​

Answer 1

Given:

One gram of protein contains 4 calories.

One gram of fat contains 9 calories.

A snack has 60 calories from p grams of protein and f grams of fat, then the equation for this relationship is

$4p + 9f = 60$

To find:

The number of grams of protein and fat in the snack.

Solution:

We have,

$4p + 9f = 60$         ...(i)

Here, we have two pairs to check, whether each pair of values could be the number of grams of protein and fat in the snack.

The pair of values which satisfies equation (i) are the possible solutions.

First pair of values: 10.5 grams of protein and 2 grams of fat.

Put p=10.5 and f=2 in equation (i).

$4(10.5)+9(2) = 60$

$42+18= 60$

$60= 60$

$LHS=RHS$

Therefore, 10.5 grams of protein and 2 grams of fat are the possible values of protein and fat.

Second pair of values: 8 grams of protein and 4 grams of fat​.

Put p=8 and f=4 in equation (i).

$4(8)+9(4) = 60$

$32+36= 60$

$68= 60$

$LHS\neq RHS$

Therefore, 8 grams of protein and 4 grams of fat​ are not the possible values of protein and fat.