Question

Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.

Short answer

First number is 2 and Second number is 3

Step-by-step solution

Given Information 

Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen.

Assume variables and frame equations

Let 'x' be the first number and 'y' be the second number

Three times a number plus three times a second number is fifteen.

3x+3y = 15

Four times the first plus twice the second number is fourteen.

4x+2y=14

solve the equations 

$$\begin{gathered} \hspace{0.17em}3x+3y\hspace{0.17em}=\hspace{0.17em}15\hspace{0.17em} \\ divideby3 \\ x+y=5 \\ y=5-x \\ \mathrm{Substitute}\mathrm{it}\mathrm{in}\mathrm{second}\mathrm{equation} \\ \hspace{0.17em}\hspace{0.17em}4x+2y=14 \\ 4x+2(5-x)=14 \\ 4x+10-2x=14 \\ 2x+10=14 \\ 2x=14-10 \\ 2x=4 \\ x=2 \\ y=5-x \\ y=5-2 \\ y=3 \end{gathered}$$

The first number is 2 and the second number is 3