Chapter 6.2, Problem 3STP

Solve each exercise and enter your answer on the grid provided.

One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?

To determine

To find:The first number of the two numbers.

Answer to Problem 3STP

The first number is 8.

Explanation of Solution

Given information:One number is 4 less than 3 times the second number. If 3 more than 2 times the first number is decreased by 2 times the second number , the result is 11.

Formula used: Use substitution method to solve the system of equations.

Calculation:

Let the one number is x and the second number is y .

The equation for one number is 4 less than 3 times the second number

  $x=3y-4$ -----(1)

The equation for 3 more than 2 times first number is decreased by 2 times second number is 11

  $2x+3-2y=11$ ------(2)

Substitute equation (1) into equation (2) for ‘ x’ .

  $2(3y-4)+3-2y=11$

Distribute to get rid the parentheses

  $6y-8+3-2y=11$

Combine like terms,

  $4y-5=11$

Add both sides 5

  $4y=16$

Divide both sides by 4.

  $y=4$

Substitute y as 4 into the equation (1)

  $x=3(4)-4$

Simplify it

  $=12-4$

  $x=8$

Hence first number is 8.