Question

As a membership fee a health club charges a one time amount of $40 and charges $25 for each month. The total fee after m months is $240. What is the value of m

A runner warms up for ten minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes. How many miles are run?

Answer 1

The first equation for the health club membership fee is 40 + 25m = 240, which solves to m = 8. The second equation for the running scenario is 10 + 7r = 45, which solves to r = 5.

Step-by-step explanation:

The student asked two separate questions related to forming equations based on a given situation. The first scenario involves a health club membership fee, and the second concerns the total time spent running given the time to run each mile and the warm-up period.

For the health club membership question, we have a one-time fee of $40 and a monthly charge of $25. The total fee after m months is $240. We can form the equation 40 + 25m = 240. To find the value of m, we subtract 40 from both sides of the equation and get 25m = 200. Then divide both sides by 25 to find that m equals 8 months.

For the running question, the runner warms up for 10 minutes and takes 7 minutes for each mile run. After running r miles, the total time is 45 minutes. The equation for this situation is 10 + 7r = 45. Subtracting 10 from both sides of the equation we get 7r = 35. Dividing both sides by 7 we find that r equals 5 miles.

Answer 2

First you need to set up an equation y = mx + b. m would be the monthly charge and b would be the one time fee. x represents the number of months.
To solve for the number of months with a total price of 240 we substitute 240 in for y and solve for x.
240 = 25x + 40
subtract 40 from each side
200= 25x
divide by 25
8 = x
8 months

10 + 7r = 45
7r = 35
r = 5
5 miles