can someone please help me with this one word problem-using system of equations?

Question

A small grocery store has a total of 26 employees. Each full time employee makes $275 per week and each part time employee makes $140 per week. If the store pays out a total of $5935 each week to its employees, how many full time and part time employees does the store have?

Answer 1

Hi Abbie D

17 Full Time

9 Part Time

Please see below

Since you are given the total number of employees and the total weekly payout, you can set up equations to represent each,

Let x = Full Time Employees

Let y = Part Time Employees

Equation 1 for total number of employees

x + y = 26

y = 26 - x

You are also given their weekly pay rates that you need for your next equation

Equation 2 for total weekly payout

275x + 140y = 5935

You can solve by Elimination or Substitution

I will multiply Equation 1 by -140 to eliminate y when I add Equation 1 to Equation2

-140x - 140y = -3640

275x + 140y = 5935

Leaving

135x = 2295

Divide both sides by 135

x = 17

y = 26 - x = 9

Checking

275(17) + 140(9) = 5935

4675 + 1260 = 5935

5935 = 5935

I hope this helps and you can try it by Substitution.

Answer 2

Let x is full time and (26 - x) part time emloyees.

Then 275x + 140(26 - x) = 5935, 55x + 28(26 - x) = 1187; 27x = 1187 - 728; 27x = 459; x = 17 full ime and

26 - 17 = 9 part time employees