Problema Solution
1. The director of a summer day camp estimates that 100 children will join if the camp fee is $350, but for each $20 decrease in the fee, ten more children will enroll.
a. Determine the linear equation that will represent the number of children who will enroll at a given fee.
b. Approximately how many students will enroll if the camp fee is $160? Round to the nearest child. Show all work for full credit.
c. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work for full credit.
2. A runner's heart rate in beats per minute is given by the formula Heart rate = 65 + 53 / (4t + 1) where t is the number of minutes after the start of a cool-down period.
Part A: Find the runner's heart rate in 10 minutes.
Part B: When is the runner's heart rate equal to 68 beats per minute?
Answer provided by our tutors
1)Let x=fee and y=number of children enrolling.
y is a linear function of x, so it can be modeled by y=mx+b, where m is the slope of the line and b is the y-intercept. m=slope=rise/run=10/-20=.5.
When x=350, y=100. So,
100=-.5*350+b
b=275.
Therefore, the line that will represent the number of children (y) who enroll at a given fee (x) is given
y=-.5x+275.
Therefore, if the fee is $160, then y= -.5*160+275=105, so 105 children will enroll.
If the fee is free, then y=-.5*0+275=275, so 275 children will enroll.
2) A runners heart rate in beats per minute is given by the formula Heart rate = 65 + 53 / (4t + 1) where t is the number of minutes after the start of a cool-down period. Find the runners heart rate in 10 minutes.
:
H.R. = 65 +
H.R. = 65 +
H.R. = 65 + 1.3
H.R. = 66.3
:
When is the runners heart rate equal to 68 beats per minute?
65 + = 68
Subtract 65 from both sides
= 68 - 65
= 3
Multiply both sides (4t+1)
53 = 3(4t+1)
53 = 12t + 3
53 - 3 = 12t
50 = 12t
t =
t = 4.2 minutes