Question

One year ago, ratio of harry and peter age's was respectively. After 4 years, this ratio becomes 6:7. How old is peter

Answer 1

let x - peter's age

y - harry's age

probably you forgot 5:6 after respectively

then

one year ago

x - 1 - peter's age one year ago

y - 1 - harry's age one year ago

then

(x-1)/(y-1)=5/6

then

(x-1)*6=(y-1)*5 (equation 1)

then

after 4 years

x + 4 - peter's age after 4 years

y + 4 - harry's age after 4 years

(x + 4)/(y+4) = 6/7

then

(x+4)*7 = (y+4)*6 (equation 2)

now we have 2 equations

(x-1)*6=(y-1)*5

(x+4)*7 = (y+4)*6

and we can find x and y from them

6*x - 6 = 5*y - 5          => 6x - 5y = 1                (1)

7*x + 28 = 6*y + 24     =>6y - 7x = 4               (2)

express x from equation 1 and substitute it to 2

6x - 5y = 1

6y - 7x = 4

x = 26 years

y = 31  year