What’s the answer

Question

An employment agency specializing in temporary construction help pays heavy equipment operators $127 per day and general laborers $98 per day. If thirty-seven people were hired and the payroll was $4148,how many heavy equipment operators were employed? How many laborers?

Answer 1

Let's label the number of heavy equipment operators as x, and the number of general laborers as y.

As such, we can see that the total number of people hired (in this case, 37), would be:

x + y = 37

The cost for hiring x number of equipment operators per day would be 127·x

The cost for hiring y number of general laborers per day would be 98·y

Payroll for hiring all contracted workers each day (in this case $4148) would therefore be:

127x + 98y = 4148

By manipulating the first equation, we can get:

x = 37 - y [we simply subtract y from both sides of the equation, and y - y cancels out on the left side]

We can then substitute this modified equation into the second equation:

127(37-y) + 98y = 4148

In order to simplify the equation and remove the parentheses, we multiply 127 by both values within the parentheses:

127··37 - 127y + 98y = 4148

4699 - 29y = 4148

4699 - 4148 -29y = 4148 - 4148 [Subtract 4148 from both sides]

551 - 29y + 29y = 29y [Add 29y to both sides]

551 = 29y

29y/29 = 551/29 [Divide all values in the equation by 29]

y = 19

Now that we have the value for y, we can solve for x using the modified equation we created earlier by substituting our known value of y:

x = 37 - 19

x = 18

We now know that 18 heavy equipment operators were hired, and 19 general laborers were hired.