1)
Amazingly, Melanie somehow remembered all of the prices for low rise
jeans among the stores. The table below
lists the stores which gave discounts or sales.
Note that the provincial sales tax in B.C. is 7.5%
|
Store |
Special |
|
|
|
|
|
Regular ($) |
|
|
Club Monica |
-- |
99.00 |
49.00 |
|
Jacobs Connections |
-- |
60.00 |
30.00 |
|
Rural Behaviour |
-- |
39.99 |
19.99 |
|
Zirens |
Buy 1 get a second for half price |
39.99 |
-- |
|
Rednotes |
All denim sale – 50% off |
49.99 |
-- |
|
New Army |
-- |
39.50 |
30.00 |
a. Find the discounts that each store offers on
one pair of jeans. Which store offers
the best discount? Sara insists that
Zirens gives the best discount because that store sells a second pair of jeans
for half the price for every one purchase.
Is her assumption correct? Why or
why not?
Calculate the discounts on 1 pair of
jeans. Extend the discount to 2 pairs of
jeans because of Ziren’s special sale.
|
Store |
Discount on 1 pair of jeans (% off) |
|
|
|
|
|
1 pair of jeans |
2 pairs of jeans |
|
Club Monica |
|
49.00 |
98.00 |
|
Jacobs Connections |
|
30.00 |
60.00 |
|
Rural Behaviour |
|
19.99 |
39.98 |
|
Zirens |
0 |
39.99 |
39.99+(39.99x0.5)=59.99 |
|
Rednotes |
50.0 |
49.99x0.5=25.00 |
50.00 |
|
New Army |
|
24.00 |
48.00 |
=50.5
=50.0
=50.0
=24.0
The discount for 2 pairs of jeans remains the
same as the discount for 1 pair of jeans in each of the stores except
Zirens.
The
discount for 2 pairs of jeans is 25% off.
If the girls were making a purchase based on the best discount alone,
then
they should shop at Club Monica which offers a 50.5% off
discount.
b. If Melanie and Sara each want two pairs of
low rise jeans for the best total price, where should they make their
purchases?
Rural Behaviour: 
=$91.55
2) Marcus and
Susie made their way to Electronix Boutique to buy some video games. They were very keen into video games and
thus, spent $78.00 (taxes included) at Electronix
Boutique. They wanted to buy an equal
number of pre-owned video games for
their PC, PS2, and Xbox.
PC games were $4.99 each, PS2 games were $2.99 each, and Xbox games were
$3.99. How many
games did they buy?
To calculate the number of games bought,
subtract the tax included into the $78.00 to get the cost before tax.
$78.00
- $78.00(GST+PST) = $78.00 – $78.00(7%+7.5%)
= $78.00 – $78.00(0.145)
= $78.00 – $11.31
= $66.69
The total cost, which is
$4.99(number of PC games) + $2.99(number of PS2 games) + $3.99(number of Xbox
games), to
be at most $66.69. Since
the numbers of PC, PS2, and Xbox games are the same (ie. they are all games),
they can all be represented by the same variable x. Then:
|
4.99x
+ 2.99x + 3.99x ≤ 66.69 |
|
4.99x
+ 2.99x + 3.99x ≤ 66.69 |
|
11.97x
≤ 66.69 |
|
x ≤ 5.57 |
Thus, they can buy x = 5 of each PC, PS2, and Xbox game.
3) The time
was nearing
near the main elevator in centre court. They were to meet their parents on the second
floor near the mall directory just above
them. They decided
to have a race to that mall directory to determine which option was faster the
elevator or escalator.
a. If the elevator was given the coordinates (0,0) and the escalator was 5 feet downwards and 84 feet to
the right of the
elevator, calculate the distance between the elevator and
escalator on the ground floor using the distance formula to 2
decimal place.
y
Elevator
distance formula = 
= 
= 
= 
= 84.15 ft
b. They decided to have a race to that mall directory to determine
which option was faster, the elevator or escalator. The
doors
to the elevator on the second floor are 26 ft away from the mall directory
whereas the top of the escalator is 9 feet
away. The elevator rises 18 ft between floors at
0.947 ft/sec. The escalator takes 27
seconds from the first to second
floor. Since Melanie and Sara walked faster, they
took the elevator while Marcus and Susie took the escalator. The race
began
when the elevator door closed. Assuming
Melanie and Sara walked at 2.8 ft/sec Marcus and Susie walked at 3.2
ft/sec,
who won the race? They all agreed not to
run.
Find the total time it takes Melanie and Sara to ride the elevator
and walk to the mall directory and likewise with Marcus
and Susie to ride the escalator and walk to the mall
directory.
Melanie and Sara:
Time for elevator = 
Time
for walking = 
= 
= 9.29 sec
= 19.0 sec
Total time = 19.0 sec + 9.29 sec = 28.29 sec
Marcus and Susie:
Time for elevator = Time
for walking = 
= 27.0 sec = 2.81 sec
Total time = 27.0 sec + 2.81 sec = 29.81
sec
Thus, Melanie and Sara win the race with a total time of 28.29
seconds.
c.
From your answer in part
b, explain whether it is more practical to take the elevator or escalator in
terms of time.
Despite favouring the elevator option in part b, the result
indicates that it would be more practical to ride the escalator.
Although the total times only differ by
nearly 1.5 sec, wait time for the elevator both getting on and getting off were
not
considered.
Several time recordings of elevator trips including wait times resulted
in traveling times well passed 19 seconds.