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=(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 } \\ (1)/(2)A+A=141-A+A \\ (3)/(2)A=141 \end{gathered}`

Step 3: Solve the system of equations for the answers

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

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