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?
Accepted Solution
A:
20 quarts of peanut oil worth 19 cents per quart must be mixed. ExplanationLets 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 [tex] =(x+100) [/tex] quarts, which will worth 24 cents per quart. Total price of x quarts oil [tex] = 19x [/tex] cents Total price of 100 quarts oil [tex] = (100*25)cents = 2500 [/tex] cents and total price of the mixture [tex] =24(x+100) [/tex] cents So the equation will be : [tex] 19x+2500 = 24(x+100)\\ \\ 19x+2500 = 24x +2400\\ \\ 19x-24x = 2400-2500\\ \\ -5x = -100\\ \\ x= \frac{-100}{-5}= 20 [/tex]So, 20 quarts of peanut oil worth 19 cents per quart must be mixed.