Question

A gym offers regular memberships for $80 per month and off-peak memberships for $60 per month. Last month, the gym sold a total of 420 memberships for a total of $31,100. How many memberships sold were regular memberships?

i get the problem i just can't understand how I'm supposed to know who was a regular member and who was a off peak member

Answer 1

@KlOwNlOvE

Answer 2

Call the $80 membership x, and the $60 membership y.

How do you express the folloing line as an equation using x and y?
"the gym sold a total of 420 memberships "

Answer 3

\[80x+60y=420\]

Answer 4

solve for x so substitute 0 in for 60 and divide 420 by 80

Answer 5

x is the number of $80 memberships sold
y is the number of $60 memberships sold

x + y represents the total number of memberships sold at both prices, right?

x + y is the total number of memberships sold.
We are told that a total of 420 memberships were sold, so that gives us one equation.

x + y = 420

For the second equation, we deal with the amount the memberships cost and the total amount of money received.

Since x represents the number of $80 memberships sold, the amount of money that was received by selling $80 memberships is 80x.

The same is true of the $60 memberships. y number of them were sold at $60 each, so the amount of money received from selling $60 memberships is 60y.

We are told the total amount of money received was $31,100. This is the info we need to find the second equation.

80x + 60y = 31100

Now we have two equations that need to be solved simultaneously.

The system of equations is:

x + y = 420
80x + 60y = 31100

Answer 6

Now we need to solve the system of equations.

Let's divide the entire second equation by 10.

x + y = 420
8x + 6y = 3110

Now let's multiply the first equation by -6

-6x - 6y = -2520
8x + 6y = 3110

Now we add the equations.

2x = 590

x = 295

Since x represents the number of $80 memberships, the answer is
295

Answer 7

^ got the last number mixed up

Answer 8

ohhhh ok

Answer 9

thank you both!