A food processing plant wants to make 1020 liters of catsup that is 30% sugar. If they have catsup that is 16% sugar and one is 50% sugar, how much of each kind should they use in the mixture?

Question

please help

Answer 1

Let a=litres of 16% catsup and b=litres of 50% catsup, then:

b=1020-a,

0.16a+0.50b=1020×0.30=306

0.16a+0.50(1020-a)=306

0.16a+510-0.50a=306

510-306=0.50a-0.16a

204=0.34a, a=204/0.34=600.

600 litres of 16% catsup and 420 litres of 50% catsup.