Question

A positive integer is divided by a smaller positive integer. The integer part of the quotient is 9 and the remainder is 1. The sum of the two integers is 71. Find the two integers

Answer 1

let the two integers be a and b (assuming a being the bigger no)
so,
a+b = 71 --------------------(1)
and a = 9*b + 1 ---------------(2)

clear till now ?

Answer 2

so far so good

Answer 3

great,
so a = 71 - b (from (1))
not sunstitute this value of a in (2)
so you get,
71 - b = 9*b + 1

now can you find b ?

Answer 4

got it

Answer 5

so what value of b did you get ?

Answer 6

7

Answer 7

good,
a = 71 - b
a = 71 - 7
a = 64

Answer 8

Solve the following equations for a and b.\[\left\{\frac{a}{b}=9+\frac{1}{b},a+b=71\right\}\]\[\{a=64,b=7\} \]