Question

A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?

Answer 1

children take 3 pieces of candy are 6

Explanation:

x+y=19-1 x+y=18

3x+5y=85-7 3x+5y=78

eliminate x by multiplying the first equation by 3:

3x+3y=54

3x+5y=85 subtract

(3x+3y)-(3x+6y)=54-78

3x-3y-3x-5y=-24

-2y=-24 y=-24/-2=12

y=12 , substitute for y:

x+y=18

x=18-12

x=6

check: 3x+5y=78

3(6)+5(12)=78

18+60=78 correct