If a number is twelve less than four times another number their difference is fifty-one what are the numbers?

Answer 1

First off the original equation would be

X - 12 = 4*y

This equations is broken down like this: a number (x) is twelve less (-12) than (=) four times (4 * ) another number (y)

The second equation comes from "Their difference (another term for subtraction) is 51"

x-y = 51

The easiest way to solve this problem would be to solve a system by substitution.

In the equation x-y = 51, add y to both sides

This would come out to x = y+ 51

Then you take this equations and substitute it in for x into the other equation

y + 51 - 12 = 4y

-4 from both sides

51 - 12 = 3y

combined like terms

39 = 3y

y = 13

Then plug back into the equation

x -12 = 13 * 4

simplify 13 * 4

x - 12 = 52

add 12 to both sides

x=64

y = 13

and

x=64