Question

URGENT!!! NEED ANSWER SOON!!!!

Pretend that you are the owner of a candy store. You have twenty pounds of cashews, which cost $3.55 a pound, and you have some peanuts, which cost $2.50 a pound. How many pounds of peanuts would you have to mix with the cashews to get a mixture that costs $3.20 per pound?

A. 10 pounds B. 9 pounds C. 7 pounds D. 8 pounds

Answer 1

10 pounds

Explanation:

So you have some given information:

(Price of cashews per pound) = 3.55

(Amount of cashes) = 20 pounds

(Price of peanuts, per pound) = 2.50

Now what you're looking for is the amount of peanuts you need to get a mixture of 3.20 per pound. So to find the price per pound. You would take the entire price and divide it by the amount of pounds. So generally it can be expressed as:
`\text{price per pound} = \frac{\text{price}}{\text{pounds}}` . In this equation we know we already have 20 pounds of cashews and they cost 3.55 per pound. We also know what the price per pound of the mixture is going to be, it's going to be 3.20. In the equation I'll express the amount of peanuts as "P" So we have the equation:

Plug in known values:

`3.20 = (20(3.55) + P(2.50))/(20+P)`

Multiply:

`3.20 = (71 + 2.5P)/(20+P)`

Multiply both sides by 20 + P

`(20+P)(3.20) = 71+2.5P`

Distribute the 3.20

`64+3.2P = 71+2.5P`

Subtract 2.5 from both side and subtract 64 from both sides

`0.7P = 7`

Divide both sides by 0.7

`P = 10`

So 10 pounds will be needed