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. 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? Choices: (A)30p + 40 = 45p - 20 (B)30p + 40 = 45p + 20 How many people would need to go zip-lining for the two options to cost the same? ____ people

Question

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. 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?   Choices: (A)30p + 40 = 45p - 20 (B)30p + 40 = 45p + 20  How many people would need to go zip-lining for the two options to cost the same?   ____ people

Bytelearn · Accepted Answer

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 = 60 / 15.

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