Question

How many pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound to produce a party mix worth $1.50 per pound?

a. 9
b. 20
c. 114.5

Answer 1

the answer is 9 pounds.

Answer 2

Answer:

9 pounds

Step-by-step explanation:

Let the amount of nuts be x

Cost of 1 pound nuts is $1.10

So, Cost of x pounds = $1.10 x

Cost of 1 pound of candy = $ 1.60

Cost of 36 pounds of candy = $1.60 \times 36=57.6$

So, total cost = 1.10 x + 57.6

Total weight = x+36

Cost of mixture per pound = $\frac{\text{total cost}}{\text{total weight}}$

Now we are given that Cost of mixture per pound is $1.50

So, $\frac{1.1x+57.6}{x+36}=1.50$

$1.1x+57.6=1.50(x+36)$

$1.1x+57.6=1.50x+54$

$57.6-54=1.50x-1.1x$

$3.6=0.4x$

$\frac{3.6}{0.4}=x$

$9=x$

Hence 9 pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound to produce a party mix worth $1.50 per pound.