Question

How many quarts of peanut oil worth 19 cents per quart must be mixed with 100 quarts worth 25 cents per quart to produce a mixture worth 24 cents per quart?

Answer 1

20 quarts of peanut oil worth 19 cents per quart must be mixed.

Step-by-step explanation

Lets assume, x quarts of peanut oil worth 19 cents per quart must be mixed.

Now we are mixing 100 quarts of another peanut oil worth 25 cents per quart with that x quarts. So, the total amount of the mixture
`=(x+100)` quarts, which will worth 24 cents per quart.

Total price of x quarts oil
`= 19x` cents

Total price of 100 quarts oil
`= (100*25)cents = 2500` cents

and total price of the mixture
`=24(x+100)` cents

So the equation will be :

`19x+2500 = 24(x+100)\\ \\ 19x+2500 = 24x +2400\\ \\ 19x-24x = 2400-2500\\ \\ -5x = -100\\ \\ x= (-100)/(-5)= 20`

So, 20 quarts of peanut oil worth 19 cents per quart must be mixed.