Question

The math team sells crunchy and fruity trail mixes to raise money. the ratio of fruit to nuts in each mix and the price they charge for an 8-oz (or 1/2-cup) bag of each mix are given in the table below. [hint: the ratio of fruit to nuts in the crunchy trail mix is 1: 3. so, 1/4 of each bag is fruit and 3/4 of each bag is nuts.] ratio of fruit to nuts price of an 8-oz (or 1/2 cup) bag crunchy trail mix 1: 3 $2.50 fruity trail mix 5: 3 $3.50 they have 30 cups of fruit and 50 cups of nuts to use in their trail mixes. so, they need to know how many bags of each type of mix they should they make. they let c represent the number of bags of crunchy trail mix and f represent the number of bags of fruity trail mix. which set of inequalities below represents the conditions? a. 1c + 3 f ≤ 30 5c + 3 f ≤ 50 c ≥ 0, f ≥ 0 b. 1c + 5 f ≤ 60 3c + 3 f ≤ 100 c ≥ 0, f ≥ 0 c. 0.25c + 0.625f ≤ 60 0.75c + 0.375f ≤ 100 c ≥ 0, f ≥ 0 d. 0.25c + 0.625f ≤ 30 0.75c + 0.375f ≤ 50 c ≥ 0, f ≥ 0

Answer 1

Answer:

(D) 0.25c + 0.625f ≤ 30 0.75c + 0.375f ≤ 50 c ≥ 0, f ≥ 0

Step-by-step explanation:

The ratio of fruit to nuts in the crunchy trail mix is 1: 3.

This means each crunchy trail mix requires $\dfrac{1}{4}=0.25$ bags of fruits and $\dfrac{3}{4}=0.75$ bags of nuts.

The ratio of fruit to nuts in the fruity trail mix is 5: 3.

This means each fruity trail mix requires $\dfrac{5}{8}=0.625$ bags of fruits and $\dfrac{3}{8}=0.375$ bags of nuts.

• Let the number of bags of crunchy trail mix=c
• Let the number of bags of fruity trail mix=f

Since the number of bags of mix cannot be negative, we have the constraints:

$c\geq 0, f \geq 0$

They have 30 cups of fruit and 50 cups of nuts to use in their trail mixes.

Therefore:

Total number of cups of fruit that can be used, 0.25c+0.625f ≤ 30

Total number of cups of nuts that can be used, 0.75c+0.375f ≤ 50

Therefore, the set of inequalities which represents the given conditions are:

0.25c + 0.625f ≤ 30 0.75c + 0.375f ≤ 50 c ≥ 0, f ≥ 0

The correct option is D.