Question

the sum of 2 numbers is 18 less than twice the first number. their difference is 32 less than twice the second number. find the numbers

Answer 1

The numbers are 43 and 25

Explanation:

Let the two numbers be x and y

the sum of these numbers is 18 less than twice the 1st number so,

`x + y = 2x-18`

simplifying,

`2x-x-18 = y\\x-18=y`

and their difference is 32 less than twice the 2nd number, so,

`x-y = 2y-32`

so,

`3y-32=x`

solving these two simultaneous equations, we have,

using y = x - 18, in the 2nd equation,

`3(x-18)-32=x\\3x-54-32=x\\3x-86=x\\2x-86=0\\2x=86\\x=43`

and then since y = x-18

`y = 43-18\\y=25`

so the numbers are 43 and 25