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

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

c) Substitute into and solve for y:

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

Explanation:

Answer 2

a)

`y=-\frac17x^2+2x+10`

`y=2x+3`

b) Equate the equations and solve for x:

`-\frac17x^2+2x+10=2x+3`

`\implies -\frac17x^2+2x-2x=3-10`

`\implies -\frac17x^2=-7`

`\implies x^2=49`

`\implies x=\pm√(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.