Question

At the beginning of a month, the number of people rock climbing increases and then decreases by the end of the month. The number of people zip-lining steadily increases throughout the same month. The models show the number of people y for each type of activity based on the number of days x since the beginning of the month.



a. Write a system of equations that represents this situation.
b. On what day or days were the same number of people rock climbing and zip-lining?
c. How many people were participating in each activity on that day or days?

Answer 1

Answer:

a)

$y=-\dfrac17x^2+2x+10$

$y=2x+3$

b)  Equate the equations and solve for x:

$-\dfrac17x^2+2x+10=2x+3$

$\implies -\dfrac17x^2+2x-2x=3-10$

$\implies -\dfrac17x^2=-7$

$\implies x^2=49$

$\implies x=\pm\sqrt{49}$

$\implies x=7$ (as time is positive)

The same number of people were rock climbing and zip-lining on day 7.

c) Substitute $x = 7$ into $y = 2x + 3$ and solve for y:

$\implies 2(7)+3=17$

Therefore, 17 people were participating in each activity on day 7.