Question

A. The sum of the two numbers is equal to 50, the subtraction of 3 times the first number and 2 times the second number is equal to 60. Find those two numbers

Answer 1

For this problem, we are given the relationship between two numbers, and we need to use this information to determine their value.

The first step is two assign variables to the two numbers, we will call them "x" and "y". We are then told that their sum is equal to 50, therefore we have:

`x+y=50`

We also are told that the subtraction of 3 times the first number and 2 times the second number is equal to 60. We can create the following expression:

`3x-2y=60`

With the two expressions we can create a system of equations:

`\begin{cases}x+y=50 \\ 3x-2y={60}\end{cases}`

We can multiply the first equation by 2 and add both to eliminate one variable:

`\begin{gathered} \begin{cases}2x+2y={100} \\ 3x-2y={60}\end{cases}\\ \\ 2x+3x+2y-2y=100+60\\ \\ 5x=160\\ \\ x=(160)/(5)=32 \end{gathered}`

The value for x is 32. We can replace x with 32 in the first expression to determine y's value:

`\begin{gathered} 32+y=50\\ \\ y=50-32\\ \\ y=18 \end{gathered}`

The value of y is 18.

The two numbers are 32 and 18.