Question

A value 4 times a smaller number is 1 more than a larger number . Their difference is 53.

Answer 1

Smaller number=18, Larger Number=71

Explanation:

Let the smaller number be s

the larger number be l

4s=1+l

4s-l=1

l-s=53

(4s-l)+(l-s)=1+53

3s=54

s=18

l-s=53

l-18=53

l=71

Answer 2

the numbers are 18 and 71

Explanation:

let x and y be the 2 numbers with x > y , then

4y = x + 1 ( subtract 1 from both sides )

4y - 1 = x → (1)

x - y = 53 → (2)

substitute x = 4y - 1 into (2)

4y - 1 - y = 53

3y - 1 = 53 ( add 1 to both sides )

3y = 54 ( divide both sides by 3 )

y = 18

and x = 4y - 1 = 4(18) - 1 = 72 - 1 = 71

the 2 numbers are 18 and 71