Solve the problem.
-Ellen wishes to mix candy worth $1.08 per pound with candy worth $3.05 per pound to form 24 pounds of a mixture worth $2.64 per pound. How many pounds of the more expensive candy should she use?
A)24 pounds
B)7 pounds
C)19 pounds
D)5 pounds

Question

Quizplus · Accepted Answer

Let x be the number of pounds of candy worth $1.08 per pound, then 24 - x is the number of pounds of candy worth $3.05 per pound. We can set up the equation:
1.08x + 3.05(24 - x) = 2.64(24)
Simplifying and solving for x, we get:
x = 19
Therefore, Ellen should use 19 pounds of candy worth $1.08 per pound and 5 pounds of candy worth $3.05 per pound to form the mixture. Let x be the number of pounds of candy worth $3.05 per pound that Ellen mixes. Then, the number of pounds of candy worth $1.08 per pound that she mixes is 24 - x.

We know that the total cost of the mixture is equal to the cost of the $3.05 per pound candy plus the cost of the $1.08 per pound candy.

So we can write:

3.05x + 1.08(24-x) = 2.64(24)

Simplifying this equation:

3.05x + 25.92 - 1.08x = 63.36

1.97x = 37.44

x ≈ 19

Therefore, Ellen should mix 19 pounds of candy worth $3.05 per pound and 5 pounds of candy worth $1.08 per pound.

Solve the Problem. -Ellen Wishes to Mix Candy Worth $1.08 Per Pound with Per