Question

A grocer wishes to mix some nuts worth 90 cents per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound. How much of each should she use?

Answer 1

He should use 75 lbs of nuts worth $0.90 and 100 lbs of nuts woth $1.60.

Explanation:

You need to use the information given to you to write two equations, one that takes into account the total weight of the nuts and one that takes into account the total price of the nuts.

First, let's label the nuts that cost `$0.90` per pound as `x` and the nuts that cost `$1.60` per pound as `y`.

This means that your first equation will be

`x + y = 175`

Now, you know that the mixture will be sold for `$1.30` per pound. This means that your second equation will be

`0.90 * x + 1.60 * y = 175 * 1.30`

Use the first equation to write `x` as a function of `y`, then take this expression and use it to find the value of `y`

`x = 175 - y`

`0.90 * (175 - y) + 1.60 * y = 227.5`

`157.5 - 0.90y + 1.60y = 227.5`

`0.70y = 70 implies y = 70/0.70 = color(green)("100 lbs")`

Now use the value of `y` to determine the value of `x`

`x = 175 - 100 = color(green)("75 lbs")`