Problem solving and using formulas

Question

You are choosing between two health clubs. Club A offers membership for a fee of $21 plus a monthly fee of $23. Club B offers membership for a fee of $28 plus a monthly fee of $22. After how many months will the total cost of each health club be the​ same? What will be the total cost for each​ club?

Answer 1

Hi Titus,

 

The easiest way to solve this is to take the unknown variable (number of months) and call that x.

 

We want to know when the cost of gym A will equal gym B.

So...

 

The cost of gym A is: 23x + 21

The cost of gym B is : 22x + 28

 

If we set these expressions equal to each other and solve for x:

23x + 21=22x + 28

1x= 7

x= 7

Therefore, in two months the cost will be the same. If we plug in 2 in either expression...

= 23(7) + 21

= 161+21

= 182

 

Each gym will cost $182 for two months of membership.

 

Hope this helps you learn how to set these up!

Answer 2

Write a system of two equations to model the situation.

Choose variables:

A total cost for club A

B total cost for club B

M number of months elapsed

A = 23 * M + 21 this models the total cost for club A ($23 per month + membership fee)

B = 22 * M + 28 this models the total cost for club B ($22 per month + membership fee)

We can solve the system by substitution or by elimination, but there is a nifty trick for this problem. Since we want the difference in cost to be zero after M months have elapsed, simply subtract the bottom equation and set it to 0:

A - B = M - 7 Set A - B to zero to get M - 7 = 0

M = 7 months

Check our work: 7 * 23 + 21 = 161 + 21 = 182 and 7 * 22 + 28 = 154 + 28 = 182

Answer 3

Hi,

m = month c = cost

A: c = 23m + 21 B: c = 22m + 28

Now your question is: total cost of each health club be the​ same

It means: 23m + 21 = 22m + 28 =====> m = 7

2)What will be the total cost for each​ club?

c = 23(7) + 21 = 182 OR 22(7) + 28 = 182 the same answer.

I hope it is useful,

Minoo