Chapter 3.4, Problem 8TFS

The goal of these matching questions is to practice step (2), Translate, of the five-step problem-solving process. Translate each word problem to a system of equations and select a correct translation from systems A–J.

$\begin{array}{l}x=y+248,\\ x+y=1094\end{array}$

$\begin{array}{l}5x=2y-3,\\ y=\frac{2}{3}x+5\end{array}$

$\begin{array}{l}y=\frac{1}{2}x,\\ 2x+2y=192\end{array}$

$\begin{array}{l}2x=7+y,\\ x+y=180\end{array}$

$\begin{array}{l}x+y=192,\\ x=2y\end{array}$

$\begin{array}{l}x+y=180,\\ x=2y+7\end{array}$

$\begin{array}{l}x-1094=y,\\ 3x-4y=248\end{array}$

$\begin{array}{l}3\%x+2.5\%y=97.50,\\ x+y=2500\end{array}$

$\begin{array}{l}2x=5+\frac{2}{3}y,\\ 3y=15x-4\end{array}$

$\begin{array}{l}x=\left(y+2.5\right)\cdot 3,\\ 3.5\left(y-2.5\right)=x\end{array}$

Mystery Numbers. Teka asked her students to determine the two numbers that she placed in a sealed envelope. Twice the smaller number is 5 more than two-thirds the larger number. Three times the larger number is 4 less than fifteen times the smaller. Find the numbers.