Question

Phoebe wants to mix raisins worth $1.60 per pound with chocolate worth $2.45 per pound to make 17 pounds of a mixture worth $2 per pound. How many pounds of raisins and how many pounds of chocolate should she use?

A) 10 pounds of raisins and 7 pounds of chocolate
B) 9 pounds of raisins and 8 pounds of chocolate
C) 8 pounds of raisins and 9 pounds of chocolate
D) 7 pounds of raisins and 10 pounds of chocolate

Answer 1

To solve this problem, set up a system of equations with two variables. Use the method of substitution to find the values of x and y. The correct answer is option B) 9 pounds of raisins and 8 pounds of chocolate.

Step-by-step explanation:

To solve this problem, we can set up a system of equations with two variables.

Let x be the number of pounds of raisins and y be the number of pounds of chocolate.

From the information given, we have the following equations:

x + y = 17 (equation 1)
1.60x + 2.45y = 2(17) (equation 2)

We can solve the system of equations by using the method of substitution or elimination.

Let's use the method of substitution.

1. Isolate x in equation 1: x = 17 - y
2. Substitute x in equation 2: 1.60(17 - y) + 2.45y = 34
3. Simplify and solve for y: 27.2 - 1.60y + 2.45y = 34 => 0.85y = 6.8 => y = 8
4. Substitute y back into equation 1: x + 8 = 17 => x = 9

Therefore, Phoebe should use 9 pounds of raisins and 8 pounds of chocolate.

So, the correct answer is option B) 9 pounds of raisins and 8 pounds of chocolate.