word problems

Question

the present age of a mother is equal to the square of her sons age. one year ago the mothers age was 7 times the age of her son at that time. Find their present ages

Answer 1

m=mother's age

s=son's age

m=s²

m-1=7(s-1)

substitute

s²-1=7(s-1)

s²-1=7s-7

s²-1-7s+7=0

s²-7s+6=0

factor

(s-6)(s-1)=0

s-6=0

s=6

m=6²=36

the mother is 36 and the son is 6

one year ago their ages were 35 and 5 and 35 is 7*5