Problem 1 :
The total cost y (in dollars) of a gym membership after x months is given by
y = 45x + 75.
What is the total cost of the membership after 9 months?
Solution :
x = number of month, y = total cost
Total cost of membership after 9 months :
When x = 9
y = 45(9) + 75
y = 405 + 75
y = 480
So, $480 is the amount for membership after 9 months.
Problem 2 :
Your annual membership fee to a nature society lets you camp at several campgrounds. Your total annual cost y (in dollars) to use the campgrounds is given by
y = 5x + 35
where x is the number of nights you camp. What do the slope and y-intercept represent?
Solution :
y = 5x + 35
x = number of nights you camp, y = annual cost
Comparing the given equation with y = mx + b, we get
the slope is 5, so cost spent per night is $5.
y-intercept = 35
So, the membership fee is $35 per year.
Problem 3 :
Bowling alleys often charge a fixed fee to rent shoes and then charge for each game you bowl. The function
C(g) = 3g + 1.5
gives the total cost C (in dollars) to bowl g games. What is the cost to rent shoes? What is the cost per game?
Solution :
C(g) = 3g + 1.5
Here slope (m) = 3 and y-intercept (b) = 1.5
Cost to rent shoes = 1.5
Cost per game = 3
Problem 4 :
You purchase a 300 minute phone card. The function
M(w) = -30w + 300
models the number M of minutes that remain on the card after w weeks. Describe how to determine a reasonable domain and range. Graph the function. How many minutes per week do you use the card?
Solution :
Let us find, x and y-intercepts to fix domain and range.
To find x-intercept, put y = 0 M(w) = 0 -30w + 300 = 0 -30w = -300 w = 10 |
To find y-intercept, put x = 0 w = 0 M(w) = -30(0) + 300 M(w) = 300 |
x-axis represents number of weeks and y-axis represents number of minutes. x and y-intercepts are (0, 300) and (10, 0).
Problem 5 :
An honor society has $150 to buy science museum and art museum tickets for student awards. The numbers of tickets that can be bought are given by 5s + 7a = 150 where s is the number of science museum tickets (at $5 each) and a is the number of art museum tickets (at $7 each). Graph the equation.
Solution :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM