Question

Select the combination of carbohydrates and fat meet the constraint

of 120 calories.
A particular diet sets a constraint of 120 calories per snack. One gram of
carbohydrates provides 4 calories. One gram of fat provides 9 calories,
The equation that models the amount of calories in the snack is
4c + 9f = 120 where c is the number of grams of carbohydrates and
f is the number of grams of fat.
4 grams of carbohydrates and 12 grams of fat
4 grams of carbohydrates and 21 grams of fat
3 grams of carbohydrates and 12 grams of fat
3 grams of carbohydrates and 13 grams of fat

Answer 1

Given:

The equation that models the amount of calories in the snack is

`4c+9f=120`

where c is the number of grams of carbohydrates and f is the number of grams of fat.

To find:

The combination of carbohydrates and fat meet the constraint of 120 calories.

Solution:

In option A, 4 grams of carbohydrates and 12 grams of fat.

Put c=4 and f=12 in the given equation.

`4(4)+9(12)=16+108=124\\eq 120`

In option B, 4 grams of carbohydrates and 21 grams of fat.

Put c=4 and f=21 in the given equation.

`4(4)+9(21)=16+189=205\\eq 120`

In option C, 3 grams of carbohydrates and 12 grams of fat.

Put c=3 and f=12 in the given equation.

`4(3)+9(12)=12+108=120`

In option D, 3 grams of carbohydrates and 13 grams of fat.

Put c=3 and f=13 in the given equation.

`4(3)+9(13)=12+117=129\\eq 120`

Only the combination of 3 grams of carbohydrates and 12 grams of fat meet the constraint of 120 calories.

Therefore, the correct option is C.