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

Setup Equation: Let's set up the equation for the total cost of zip-lining for p people at Blackberry Lake and Mount Oak, respectively. At Blackberry Lake, the cost is $30 per person plus a $40 equipment fee. At Mount Oak, the cost is $45 per person minus the $20 coupon. The equation to represent this scenario is: Total cost at Blackberry Lake = Total cost at Mount Oak 30p + 40 = 45p - 20 (after applying the coupon at Mount Oak)Solve for p: Now we need to solve for p. To do this, we will first move all terms involving p to one side of the equation and the constant terms to the other side. We can subtract 30p from both sides to get: 30p + 40 - 30p = 45p - 20 - 30p This simplifies to: 40 = 15p - 20Isolate Variable p: Next, we will isolate the variable p by moving the constant terms to the other side. We add 20 to both sides of the equation: 40 + 20 = 15p - 20 + 20 This simplifies to: 60 = 15pDivide to Solve: Finally, we divide both sides by 15 to solve for p: 60 / 15 = 15p / 15 This simplifies to: 4 = p

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