Question

Three times one number is 8 more than 2 time the second number. The sum of the two numbers is 40. Find the numbers

Answer 1

`x=(88)/(5)\text{ and }y=(112)/(5)`

Step-by-step explanation:

Let's say the first number in question is x and the second number is y.

`\begin{gathered} 3x=8+2y \\ x+y=40 \end{gathered}`
`\begin{gathered} x+y=40 \\ y=40-x\text{ or }x=40-y \end{gathered}`

After isolating one value, replace it in the other equation.

`\begin{gathered} 3x=8+2(40-x) \\ 3x=8+80-2x \\ 5x=88 \\ x=(88)/(5) \end{gathered}`

Now do the same for the other value;

`\begin{gathered} 3(40-y)=8+2y \\ 120-3y=8+2y \\ 112=5y \\ y=(112)/(5) \end{gathered}`

To make sure you have the right answers, double-check by replacing both values in one of the equations and check to see if the equality is true:

`\begin{gathered} (88)/(5)+(112)/(5)=40? \\ (200)/(5)=40\text{ : true} \end{gathered}`

Since it is true, your 2 numbers are 88/5 and 112/5.