Question

how can I translate this word problem into a system of equations for solving the problem? one number is half another number. the sum of the two numbers is 141. find the numbers?

Answer 1

Find the missing numbers:

Step 1: Restate the applied problem.

Let A and B be numbers such that B = 1/2 A and A+B = 141

$\begin{gathered} B=\frac{1}{2}A \\ A+B=141 \\ B=141-A \end{gathered}$

Step 2: Translate the words into a system of equations for solving the problem.

Since B = 1/2A use that fact to rewrite 1/2A = 141 - A.

$\begin{gathered} \text{Add A to both side } \\ \frac{1}{2}A+A=141-A+A \\ \frac{3}{2}A=141 \end{gathered}$

Step 3: Solve the system of equations for the answers

$\begin{gathered} \frac{3}{2}A=141 \\ 3A=141(2) \\ A=\frac{282}{3} \\ A=94 \\ B=\frac{1}{2}A=\frac{94}{2}=47 \end{gathered}$

Therefore the correct answer for the missing numbers are 47 and 94