Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ 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? $\newline$ If Bill attends $\square$ classes per month, each membership plan costs $\$$ $\square$ $\newline$ Submit

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

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?

\newline

If Bill attends

\square

classes per month, each membership plan costs

\$

\square

\newline

Submit

Cost Equations: Let's call the number of classes Bill attends ＂x＂. For the first membership plan, the cost is $\$60$ plus $\$1$ per class. So the cost equation for the first plan is: $\newline$ $C_1 = 60 + x$
Set Equations Equal: For the second membership plan, the cost is $\$6$ plus $\$3$ per class. So the cost equation for the second plan is: $\newline$ $C_2 = 6 + 3x$
Solve for x: We want to find when $C_1$ equals $C_2$ , so we set the equations equal to each other: $60 + x = 6 + 3x$
Calculate Total Cost: Now we solve for $x$ . Subtract $x$ from both sides: $\newline$ $60 = 6 + 2x$
Calculate Total Cost: Now we solve for $x$ . Subtract $x$ from both sides: $\newline$ $60 = 6 + 2x$ Subtract $6$ from both sides: $\newline$ $54 = 2x$
Calculate Total Cost: Now we solve for $x$ . Subtract $x$ from both sides: $\newline$ $60 = 6 + 2x$ Subtract $6$ from both sides: $\newline$ $54 = 2x$ Divide both sides by $2$ to find $x$ : $\newline$ $x = 27$
Calculate Total Cost: Now we solve for $x$ . Subtract $x$ from both sides: $\newline$ $60 = 6 + 2x$ Subtract $6$ from both sides: $\newline$ $54 = 2x$ Divide both sides by $2$ to find $x$ : $\newline$ $x = 27$ Now we need to find the total cost for $27$ classes. We can plug $x$ into either $x$ $0$ or $x$ $1$ since they are equal: $\newline$ $x$ $2$
Calculate Total Cost: Now we solve for $x$ . Subtract $x$ from both sides: $\newline$ $60 = 6 + 2x$ Subtract $6$ from both sides: $\newline$ $54 = 2x$ Divide both sides by $2$ to find $x$ : $\newline$ $x = 27$ Now we need to find the total cost for $27$ classes. We can plug $x$ into either $C_1$ or $C_2$ since they are equal: $\newline$ $x$ $0$ Calculate the total cost: $\newline$ $x$ $1$