INTERPRETING LINEAR EQUATION WORD PORBLEMS

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.

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 :