Question

The sum of two numbers is 167. The second number is 29 less than three times the first number. Fine the numbers. The two required numbers are:

Answer 1

`\Huge \boxed{\mathrm{49 \ and \ 118}}`

Explanation:

Let the first number be
`x`

Let the second number be
`y`

`x+y=167`

`y=3x-29`

Applying substitution method.

`x+3x-29=167`

Combining like terms.

`4x-29=167`

Adding 29 to both sides.

`4x=196`

Dividing both sides by 4.

`x=49`

Substituting x = 49 for the second equation.

`y=3(49)-29`

Multiplying the numbers.

`y=147-29`

Subtracting.

`y=118`

The two required numbers are 49 and 118.

Answer 2

49 and 118

Explanation:

Let the two numbers be x and y

x+y = 167

y = 3x-29

Substitute into the first equation

x+ 3x-29 = 167

Combine like terms

4x - 29 = 167

add 29 to each side

4x = 167+29

4x = 196

Divide by 4

4x/4 = 196/4

x = 49

x+y = 167

49+y = 167

y = 167-49

y =118