Question

The sum of two numbers is 35. The larger number is one less than three times the smaller number. Let represent the larger number. Let represent the smaller number. Write a system of equations to represent this situation. What are the two numbers?

Answer 1

Step-by-step explanation

To solve the question we will have to set up a simultaneous equation

If x represents the larger number

y represents the smaller number, then

The sum of the two numbers is 35

`Equation\text{ 1: x+y=35}`

The larger number is one less than three times the smaller number.

`Equation\text{ 2: }x=3y-1`

So, we will solve the equation using the substitution method

Thus, we will substitute x = 3y -1 into equation 1

`\begin{gathered} 3y-1+y=35 \\ 3y+y-1=35 \\ 4y-1=35 \\ 4y=35+1 \\ 4y=36 \\ \\ y=(36)/(4) \\ \\ y=9 \end{gathered}`

The smaller number is 9

The larger number will be

`\begin{gathered} x+y=35 \\ x=35-y \\ x=35-9 \\ x=26 \end{gathered}`

The larger number is 26

The answers are 9 and 26