Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Bill wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Bill can pay $60 per month, plus $1 for each group class he attends. Alternately, he can get the second membership plan and pay $6 per month plus $3 per class. If Bill attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount? If Bill attends ◻ classes per month, each membership plan costs $ ◻.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Bill wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Bill can pay $60 per month, plus  $1 for each group class he attends. Alternately, he can get the second membership plan and pay $6 per month plus $3 per class. If Bill attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount? If Bill attends ◻ classes per month, each membership plan costs $ ◻.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: Let x be the number of classes Bill attends per month. Let y be the total cost for each membership plan.  For the first membership plan: The total cost is $60 plus $1 per class. So the equation for the first plan is: y = 60 + 1xFirst Membership Plan: For the second membership plan: The total cost is $6 plus $3 per class. So the equation for the second plan is: y = 6 + 3xSecond Membership Plan: Now we need to find the number of classes (x) where the cost of both plans is the same. This means we set the two equations equal to each other: 60 + 1x = 6 + 3xSet Equations Equal: To solve for x, we'll subtract 1x from both sides: 60 = 6 + 2xSubtract 1x: Now, subtract 6 from both sides to isolate the term with x: 54 = 2xIsolate Term with x: Divide both sides by 2 to solve for x: x = 27Solve for x: Now that we have the value for x, we can substitute it back into either of the original equations to find the total cost (y). We'll use the first equation: y = 60 + 1x y = 60 + 1(27)Substitute x Value: Calculate the total cost: y = 60 + 27 y = 87

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