Question

One third of a number decreased by the second number equals 11. One third of the first number increased by the second number is equal to 1. What are the numbers?

Answer 1

let the first number is a

the second number is b

so, it is given One-third of a number decreased by the second number equals 11,

`(a)/(3)-b=11`

also, One-third of the first number increased by the second number is equal to 1.

`(a)/(3)+b=1`

add both the equation

`\begin{gathered} 2*(a)/(3)=12 \\ a=18 \end{gathered}`

so the first number is a = 18

put a = 18 in the first equation

`(18)/(3)-b=12`
`\begin{gathered} 6-b=12 \\ b=6-12 \\ b=-6 \end{gathered}`

so the second number is -6

so the numbers are 18 & -6