Question

Two-thirds of a number is two more than one-half of another number. The sum of the number is 129. Find the numbers.​

Answer 1

Answer: 57 ; 72

Step-by-step explanation:

Given information

2/3 of a number is 2 more than (1/2) of another number

Sum = 129

Set variables

Let x be the first number

Let y be the other number

Set system of equations

`1)~(2)/(3) x=(1)/(2) y+2`

`2)~x + y=129`

Eliminate fractions in the 1) equation

`(2)/(3) x*6=(1)/(2) y*6+2*6`

`4x=3y+12`

Move x and y onto the same side

`4x-3y=12`

Current System

`1)~4x-3y=12`

`2)~x + y=129`

Multiply 3 on both sides in 2) equation

`x*3 + y*3=129*3`

`3x+3y=387`

Current System

`1)~4x-3y=12`

`2)~3x+3y=387`

Add 1) equation and 2) equation together

`(4x - 3y)+(3x+3y)=(12)+(387)`

Expand parenthesis and combine like terms

`4x - 3y + 3x + 3y = 12 + 387`

`4x + 3x - 3y + 3y=399`

`7x=399`

Divide 7 on both sides

`7x/7=399/7`

`\Large\boxed{x=57}`

Substitute the x value into one of the equations to find the y value

x + y = 129

(57) + y = 129

y = 129 - 57

`\Large\boxed{y=72}`

Hope this helps!! :)

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