# Linear Relations: Question Preview (ID: 18262)

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The total cost of swimming at a community swimming pool is made up of a membership fee and a cost per swim. At this community centre, Jake pays a total of \$100 and swims 40 times. Paula pays a total of \$70 and swims 25 times. Which of these is true?
a) The membership fee is \$20.
b) The membership fee is \$30.
c) The membership fee is \$2.50.
d) The membership fee is \$2.80.

Alex's Rose Shop makes up bouquets and charges for the vase, plus a cost per rose. The shop charges \$32.85 for a bouquet of 12 roses, and charges \$50.85 for a bouquet of 20 roses. What does Alex's Rose Shop charge for a vase?
a) \$18.00
b) \$8.00
c) \$5.85
d) \$2.74

The total cost of hiring Beth's Plumbing Services is represented by the equation C = 50t + 70, where C is the total cost in dollars and t is the time in hours. Next month, the rate will change to \$60 per hours, but the initial charge stays the same.
a) The new graph of the relation will change - the steepness of the line will increase
b) The new graph of the relation will change - the steepness of the line will decrease
c) The new graph of the relation will change - the vertical intercept will increase by 10 units
d) The new graph of the relation will change - the vertical intercept will decrease by 10 units

Nadia lives 11.4km from school and walks every day. The equation d = 11.4 - 0.6t represents the relationship between d, her distance from school in km, and t, her time travelling in minutes. If she leaves home at 8:05AM, when will she get to school?
a) 8:11 AM
b) 8:16 AM
c) 8:17 AM
d) 8:24 AM

The cost, C, in dollars to print n leaflets is given by the formula C = 0.35 + 0.03n. What is the cost of printing 900 leaflets?
a) \$27.00
b) \$35.00
c) \$37.70
d) \$62.00

Liam sells sandwiches at an arena. He earns \$10.50 per hour plus \$0.40 for each sandwich he sells. How many sandwiches does he need to sell during a 6-hour shift to earn \$125?
a) 158
b) 155
c) 62
d) 12

A sports company uses the equation C = 8t + 5 to represent the relationship between the total amount charged to rent a canoe, C, in dollars and the rental time, t, in hours. What is the initial charge to rent a canoe?
a) \$0
b) \$5
c) \$8
d) \$13

Karina has a job and gets paid each week with an hourly rate plus \$14 for transportation. One week she works 20 hours and is paid \$215. Which equation represents the relationship between her total pay, P, and the number of hours she works, n?
a) P = 10.75n + 14
b) P = 14n + 10.75
c) P = 10.05n + 14
d) P = 14n + 10.05

Charges on a monthly water bill are \$0.86 per meter cubed of water used plus a service charge of \$4.49. Let C = total charge, in dollars, and w = total amount of water used, in meters cubed. Which equation represents the relationship between C and w?
a) C = 4.49 X 0.86w
b) C = 4.49w + 0.86
c) C = 4.49 + 0.86w
d) C = (4.49 + 0.86)w

Student council sells lollipops for \$0.10 each. They pay \$0.04 for each lollipop and spend \$10 to advertise. P represents the student council's profit, in dollars, and n represents the number of lollipops sold. Which equation represents the profit?
a) P = 0.06n - 10
b) P = 0.06n + 10
c) P = 10n + 0.06
d) P = 10 + 0.04n

Alex has \$150. She spends the same amount each week. After 6 weeks, she has \$30 remaining. The relationship between the amount of money Alex has and the number of weeks is represented by a line. What is the slope of this line?
a) -25
b) -20
c) 20
d) 25

Identical bottles are packed in a box. The box will hold a maximum of 38 bottles. The relationship between M, the total mass of the box and contents, and n, the number of botles in the box, is represented by the equation M = 500n + 800.
a) Possible values of n are: n is greater than 37
b) Possible values of n are: n is greater than or equal to 0
c) Possible values of n are: n is greater than 0 but less than 39
d) Possible values of n are: n is greater than or equal to 0 but less than 39

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