# The sum of two numbers is 44. If the larger number is two less than three times the smaller number, find the numbers.

beckden | High School Teacher | (Level 1) Educator

Posted on

Translate into equations x is one number y is the other.  Let's say y is the larger number.

x+y=44

and

y=3x-2

Using substitution we get

x+3x-2=44

4x=46

x=11.5

y=44-x=32.5

check 3(11.5)-2=34.5-2=32.5

So the two numbers are 11.5 and 32.5

hcteach | High School Teacher | (Level 1) Adjunct Educator

Posted on

Lets say the numbers are x and y. The two equations are:

x+y=44

x= 3y-2

Next you use substitution for x in the first equation which brings you to 3y-2 + y = 44 which simplyfies to:

4y - 2 = 44

4y = 46

y = 11.5

Then you plug back y=11.5 in either of the equation to solve for x:

x = 3y - 2

x = 3(11.5) - 2

x = 32.5

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The sum of two numbers is 44. If the larger number is two less than three times the smaller number, find the numbers.

x+y=44

and

y=3x-2

plug in the numbers as y in the first problem:

x + 3x - 2 =44

combine like terms

x + 3x = 44 + 2

4x = 46

divide by 4

x = 11.5