Question

Dominic is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $50 and the one-time joining fee is $150. How many months would it take for the cost to be $550?

Answer 1

Concept:

This relationship describes a function, which occurs when one quantity (or variable) affects another quantity (or variable). This can be mathematically described as: y is a function of x, or for x input, y output is the result.

Solving:

We know the relationship is linear because it gives us a rate of increase. This rate is $50/month. We also are given a starting point of $150 because that is the fee for simply joining.

Therefore, we can use the linear function form: y=mx+b. Let’s define the variables:

y = total after “x” months

m = slope (or rate of change)

x = # of months

b = starting point

So, we have y=mx+b. Now, let’s substitute the information in for the corresponding variables:

(550)=50x+(150)

Now, let’s solve for x:

Subtract 150 from both sides:

550-150=50x

Divide both sides 50:

400=50x

8=x

Apply the symmetric property:

x=8

So, the answer is 8 months

Answer 2

Answer: 8

Step-by-step explanation: 550-150=400, 400/50=8