You are choosing between two gyms. One gym offers membership f...

Question

You are choosing between two gyms. One gym offers membership for a fee of $40 plus a monthly fee of $25. The other offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

Accepted Answer

Hello. Today we're going to be solving this type of word problem. So the problem states that you want to learn cooking by enrolling in a culinary training center this summer. The first center offers a one time registration fee of $ and an hourly fee of $5. The second center offers a one time registration fee of $20 and an hourly fee of $8. We want to go ahead and figure out how many hours it will take for the cost to be the same at both centers and we want to know what's the total cost at this amount of hours. So let's just go ahead and keep two things in mind. We have two centers are offering different rates. The first center offers a one time registration fee of $50 and an hourly fee of $5. So we're gonna go ahead and label Centre one. The total cost of this is going to be $50 plus $5 times the amount of hours that you're going to be spending at the center. Now again, you can spend any amount of hours you want. So we can represent the hours as the variable x. Now, the second center offers a one time registration fee of $20 and an hourly fee of $8. So for center too, It has a one time registration fee of $20 plus eight times the amount of hours that you're going to be spending at the center, which is X. Now we want to go ahead and find out what's the amount of hours we need to spend at each center in order for both of the costs to be the same. Well in order to figure that out, we want to go ahead and equate both of these amounts together. So what we end up with is 50 plus five X equal to 20 plus eight X. And if we solve for X this is going to give us the amount of hours that we need to spend at both centers for the cost to be the same. So in order to start this, let's go ahead and subtract 20 from both sides of this equation. Doing so is going to give us 30 plus five X is equal to eight X. Next let's go ahead and subtract five X from both sides. Doing so is going to give me 30 equal to three X. And finally, in order to solve for X, we're going to go ahead and divide both sides of this equation by three. Doing so is going to give me X is equal to 10. What this means is we need to spend 10 hours at each center in order for the cost to be the same. Now we need to figure out what that cost is. Well, since the costs are going to be the same, we can go ahead and plug in this amount of X to either equation and doing so should give us the same amount at both. So let's go ahead and plug in 10 to center one. Now center once price is represented as 50 plus five X. But we're gonna be replacing X with the value of 10. So 50 plus five times 10 is going to be 50 plus 50 and 50 plus 50 is going to produce a total value of 100. So that's gonna be the total cost at center one. Now if we plug in this value into center to it should give us the same cost. So center two's price is represented as 20 plus eight times the amount of hours which is going to be 10 8 times 10 gives us 80. So 20 plus 80 is equal to 100. So the prices match And the amount of hours which is 10 hours produces a total cost of 100. So the solution is going to be 10 hours for $100. And that means that the answer to this problem is going to be D So I hope this video helps you in understanding how to solve this type of word problem. And I'll go ahead and see you all in the next video

You are choosing between two gyms. One gym offers membership for a fee of \$40 plus a monthly fee of \$25. The other offers membership for a fee of \$15 plus a monthly fee of \$30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

Key Concepts

Linear Equations

Setting Equations Equal to Find Intersection

Substitution to Find Total Cost

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