Question

Ann wants to mix a tomato sauce that is 17% sugar with a sauce that is 30% sugar to obtain 2.6 quarts of a tomato sauce that is 24% sugar. How much of each should she mix?

Answer 1

she should mix 1.2 quarts of sauce with 17% sugar with 1.4 quarts of sauce with 30% sugar

Explanation:

X= quarts of sauce # 1 ( 17% of sugar)

Y= quarts of sauce # 2( 30 % of sugar )

General Balance

`X+Y=2.6` EQ (1)

`Y=2.6-X\\`

SUGAR BALANCE

`0.17X+0.3Y=2.6*0.24\\` EQ (2)

replace Y from eq(1) into eq(2)

`0.17X+0.3(2.6-X)=0.624\\0.17X+0.78-0.3X=0.624\\-0.13X=0.624-0.780\\X=(-0.156)/(-0.13) \\X= 1.2\\Y=2.6-1.2=1.4`