Question

Three times a number is subtracted from another number and the difference is 3. The sum of the two numbers is 31. What is the smaller of the two numbers

Answer 1

7

Explanation:

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

y - 3x = 3 → (1)

x + y = 31 → (2)

Rearrange (1) expressing y in terms of x by adding 3x to both sides

y = 3 + 3x → (3)

Substitute y = 3 + 3x into (2)

x + 3 + 3x = 31, that is

4x + 3 = 31 ( subtract 3 from both sides )

4x = 28 ( divide both sides by 4 )

x = 7

and y = 3 + (3 × 7) = 3 + 21 = 24

The smaller of the 2 numbers is 7