Question

A store is mixing peanuts, which cost $3.20 per pound, and raisins, which cost $2.10 per pound.

How many pounds of peanuts and raisins should be used to make a mix that costs $44.50 and weighs 17 pounds?


___ lb peanuts

___lb raisins

Answer 1

Answer: 8 lb of peanuts and 9 lb of raisins

Explanation:

Answer 2

The store mixes 8 pounds of peanuts and 9 pounds of raisins.

Explanation:

Let the store mixes 'x' pounds of peanuts and 'y' pounds of raisins.

The cost of peanut per pound is $3.20 and cost of raisins per pound $2.10

According to question,

Total weight of mixture given is 17 pounds.

`\Rightarrow x+y=17` ................(1)

also total cost of mixture given is $44.50

`\Rightarrow 3.20x+2.10y=44.50` ...........(2)

Solving for equation (1) and (2),

Multiply equation (1) by 3.20 , we get

(1)⇒
`3.20x+3.20y=54.40` ............(3)

Now, subtract equation (3) from equation (2) , we get

`3.20x+2.10y-(3.20x+3.20y)=44.50-54.40`

`\Rightarrow 3.20x+2.10y-3.20x-3.20y=-9.90`

`\Rightarrow 2.10y-3.20y=-9.90`

`\Rightarrow -1.1y=-9.90`

`\Rightarrow y=9`

Thus, The store mixes 9 pounds of raisins.

Put, y = 9 in (1),

`\Rightarrow x+y=17 \Rightarrow x+9=17 \Rightarrow x=8`

Thus, The store mixes 8 pounds of peanuts.