Please help!

A gym offers a 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?

A. 125
B. 140
C. 235
D. 295

Question

Please help! 

A gym offers a 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?

A. 125
B. 140
C. 235
D. 295

anonymous · Answer

a

doggy · Answer

http://openstudy.com/study#/updates/5261a7afe4b0c23cd54aecde I found this, i'm not sure if it will answer your question but i believe it might... I hope it does

anonymous · Answer

Oh, I saw that one. It only confuses me more. :/

mathstudent55 · Answer

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 "

anonymous · Answer

I have no idea. :/

mathstudent55 · Answer

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?

anonymous · Answer

Right.

anonymous · Answer

Hello?

mathstudent55 · Answer

Sorry, I lost the connection.

Ok, let's get back to the problem.

mathstudent55 · Answer

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

mathstudent55 · Answer

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

mathstudent55 · Answer

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

anonymous · Answer

Oh, I ended up finishing the problem myself, but thanks anyways. I got the same number.

mathstudent55 · Answer

Great. You're welcome.