4.11 Consumer applications of proportional reasoning
State whether each table represents a proportional relationship:
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 2 | 4 | 6 | 8 | 10 |
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | 7 | 14 | 6 | 28 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 2 | 4 | 6 | 8 | 17.5 |
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | 1.5 | 3 | 4.5 | 6 |
| x | 1 | 2 | 3 | 4 | 6 |
|---|---|---|---|---|---|
| y | 90 | 180 | 270 | 360 | 540 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 3 | 7 | 11 | 15 | 22 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 10 | 20 | 30 | 45 | 50 |
Consider the points that have been plotted on the coordinate plane:
Determine whether a straight line can be drawn through all the points.
Find the increase in y from x = 1 to \\x = 2.
Find the increase in y from x = 2 to \\x = 3.
Is y increasing at a constant rate?
Is y proportional to x?
Consider the following table of values.
If x doubles in value, does y also always double in value?
Find the increase in y for every 1 unit increase in x.
Is y increasing at a constant rate?
Do the values of x and y satisfy an equation of the form y = k x for some constant k?
Is y proportional to x?
| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |
Consider the points that have been plotted on the coordinate plane:
Determine whether a straight line can be drawn through all the points.
Find the increase in y when x increases from x = 1 to x = 2.
Is y increasing at a constant rate?
Find y when x = 0.
Is y proportional to x?
A courier’s delivery charges are outlined in the table below.
| \text{Weight of parcel (lb)} | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| \text{Cost (dollars)} | 5.10 | 9.20 | 12.30 | 14.40 |
If a parcel weighs 2 \text{ lb}, find the cost per \text{lb} of sending the parcel.
If the parcel weighs 4 \text{ lb}, find the cost per \text{lb} of sending the parcel.
Is the cost of delivery proportional to the weight of the parcel?
A physiotherapist charges \$55 per patient she treats. The table shows her weekly income in weeks where she treated 25 and 42 patients.
| Number of patients seen in the week | 12 | 25 | 32 | 42 | 51 |
|---|---|---|---|---|---|
| Weekly income (dollars) | 1375 | 2310 |
Complete the table.
How much would she earn in a week where she treated 0 patients?
Is her weekly income proportional to the number of patients she sees in that week?
The admission prices to an amusement park are set out in the table below.
If you enter as part of a family, how much would each person’s admission cost?
Is the admission price proportional to the number of people?
| Admission Price | |
|---|---|
| 1 \text{ Adult} | \$30 |
| \text{Family (} 4 \text{ people)} | \$107 |
| \text{Group (} 10 \text{ people)} | \$270 |
The cost of parking for various amounts of time was recorded at 4 different locations in the city.
Find the cost per hour for the location where parking cost \$13.50.
Is x proportional to y?
| \text{Number of hours } (x) | \text{Cost of parking } (y) |
|---|---|
| 3 | \$13.50 |
| 3.5 | \$16.75 |
| 12 | \$54.00 |
| 8 | \$34.50 |
At a ski resort, you can purchase lift passes according to the number of days you wish to ski. For example, if you want to ski for 3 days you could purchase a 3 day lift pass, or a 2 day lift pass and then a 1 day lift pass. The lift pass prices are shown on the graph.
Find the cost for the following:
1 day lift pass
3 day lift pass
Find the cost each day for the following:
4 day lift pass
6 day lift pass
Determine whether a straight line can be drawn so that it goes that it goes through all the points.
Is the lift pass price proportional to the number of days it is used?
If you want to ski for 5 days, would you be better off purchasing a 5 day lift pass or a 1 day lift pass each day for 5 days?
The resort has a special offer whereby if you purchase a 7 day lift pass, you get an extra day lift access for free. If you purchase this deal, how much would it cost per day?
Consider the points that have been plotted on the coordinate plane:
Find the parking cost oper hour for the following number of hours:
5 hours
9 hours
Regardless of how long you park for, does the hourly cost of parking remain the same?
Determine whether a straight line can be drawn through all the points.
Find the value of y when x = 0.
Is y proportional to x?
In the following table, y represents the total rent paid on a house that has been rented for x weeks.
Find the weekly cost of rent.
Find the value of y when x=0.
Write an equation for y in terms of x.
| x | y |
|---|---|
| 10 | 3350 |
| 20 | 6700 |
| 30 | 10,050 |
| 40 | 13,400 |
| 50 | 16,750 |
The plotted points show the cost, in dollars, of printing x digital photos.
How much would it cost to print 0 photos?
Determine whether the cost per photo is the same for any quantity of photos.
Determine whether it is possible to draw a straight line that goes through all the points.
Determine whether the the cost of printing digital photos is proportional to the number of photos printed.
Find the cost of printing 70 digital photos.
A car dealership has received 88 of the latest model Subaru. The dealership hopes to have sold all of them within 11 weeks.
The number sold by the end of the second and fourth weeks is shown in the table. Assuming the new Subarus are being sold at a constant rate, complete the table.
| \text{Week }(w) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Number sold }(n) | 12 | 24 |
Form an equation relating w and n.
If the new models continue to be sold at this rate, find the number of units sold in 11 weeks.
Find the number of the new models that will remain after 11 weeks.
How many new models would they have had to sell each week to have had them all sold in 11 weeks?
James wants to buy cereal, and sees that a 500 gram box is priced at \$6.05.
Find the unit price of the cereal per 100 grams.
Form an equation relating the cost of the cereal, y, to the weight of the cereal box in grams, x.
James sees that a 750 \text{ g} box of the same cereal is priced at \$8.18. Opting for the larger box, find the saving per 100 grams.
Jenny and Amelia have used two different investment strategies to enhance their savings. The amount of interest Amalia has earned after t years is presented in the table and the amount of interest Jenny has earned is presented in the graph.
Whose interest earns proportionally to the number of years passed?
Form an equation for y, the amount of interest Amelia earned, after t years.
Jenny withdraws her money when she has earned a total of \$120 interest.
Find the number of years, t, that Amelia will need to invest her money to earn the same amount of interest.
Amelia's Interest Earned
| \text{Years } (t) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \text{Interest earned } (y) | 0 | 8 | 16 | 24 |
Jenny's Interest Earned
Consider the two following investment methods:
Method A: Deposit \$4000 into an account immediately, and add \$40 at the end of each month thereafter.
Method B: Deposit \$80 at the end of each month.
Complete the table of values for the total amount of the investment after t months under each method of investment:
| \text{Month } (t) | 1 | 2 | 3 | 4 | 5 | 6 | 12 |
|---|---|---|---|---|---|---|---|
| \text{Method A (dollars)} | |||||||
| \text{Method B (dollars)} |
Under which investment method would the total investment amount be proportional to the number of months passed?
Which method will lead to a greater amount invested after 15 months?
Which method will lead to a greater amount invested after 102 months?