Liz is comparing two options to go zip-lining with some friends. The zip line at Blackberry Lake costs $\$30$ per person, plus a $\$40$ charge to rent equipment for the group. The zip line at Mount Oak costs $\$45$ per person, with no additional charge for equipment. Liz also has a coupon for $\$20$ off the total price at Mount Oak. $\newline$ Which equation can you use to find $p$ , the number of people who would need to go zip-lining for the two options to cost the same? $\newline$ Choices: $\newline$ (A) $30p + 40 = 45p - 20$ $\newline$ (B) $30p + 40 = 45p + 20$ $\newline$ How many people would need to go zip-lining for the two options to cost the same? $\newline$ $\_\_\_$ people $\newline$

Full solution

Q. Liz is comparing two options to go zip-lining with some friends. The zip line at Blackberry Lake costs

\$30

per person, plus a

\$40

charge to rent equipment for the group. The zip line at Mount Oak costs

\$45

per person, with no additional charge for equipment. Liz also has a coupon for

\$20

off the total price at Mount Oak.

\newline

Which equation can you use to find

p

, the number of people who would need to go zip-lining for the two options to cost the same?

\newline

Choices:

\newline

(A)

30p + 40 = 45p - 20

\newline

(B)

30p + 40 = 45p + 20

\newline

How many people would need to go zip-lining for the two options to cost the same?

\newline

\_\_\_

people

\newline

Set Up Equation: First, let's set up the equation to compare the costs of both zip-lining options. Blackberry Lake costs $\$30$ per person plus a $\$40$ group equipment fee, so the total cost for $p$ people is $30p + 40$ . Mount Oak costs $\$45$ per person, but Liz has a $\$20$ coupon, so the total cost for $p$ people is $45p - 20$ . The equation to find when both costs are the same is $30p + 40 = 45p - 20$ .
Solve Equation: Step $1$ : Now, solve the equation $30p + 40 = 45p - 20$ . First, subtract $30p$ from both sides to get all terms involving $p$ on one side: $40 = 15p - 20$ .
Solve Equation: Step $2$ : Next, add $20$ to both sides to isolate the term with $p$ : $60 = 15p$ .
Solve Equation: Step $3$ : Finally, divide both sides by $15$ to solve for $p$ : $p = \frac{60}{15}$ .