# 7-4 Applications of Linear Systems

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```					   Applications of Linear Systems
1. It costs \$11.46 for 4 hamburgers and 6
milkshakes and \$2.47 for 2 hamburgers and 1
milkshake. Determine the cost of 1
hamburger and 1 milkshake.
It costs \$11.46 for 4 hamburgers and 6 milkshakes and \$2.47 for 2 hamburgers and 1
milkshake. Determine the cost of 1 hamburger and 1 milkshake.
h= cost of a hamburger
m = cost of a milkshake
4h + 6m = \$11.46
2h + m = \$2.47
8h + 12m = \$22.92
-8h -4m = - 9.88
8m = \$13.04
m = \$1.63,      2h + 1.63 = 2.47, 2h = 0.84
h=\$0.42 (0.42, 1.63)
check 4(0.42) + 6(1.63) = 11.46
1.68 + 9.78 = 11.46 11.46=11.46
page 198 # 1
The width of a rectangles is 14 inches less than
the length. The perimeter of the rectangle is 92
inches. Define the two variables and write two
equations.
The width of a rectangles is 14 inches less than
the length. The perimeter of the rectangle is 92
inches. Define the two variables and write two
equations.
w = width
l = length
w=l – 14
2w + 2l = 92
page 198 # 2 - SOLVE
The price of a sweater is \$5 less than twice the
price of a shirt. If four sweaters and three shirts
costs \$200, find the price of each shirt and each
sweater.
The price of a sweater is \$5 less than twice the price of a shirt. If four sweaters and three shirts
costs \$200, find the price of each shirt and each sweater.

a = price of sweater
b = price of shirt
a = 2b - 5
4a + 3b = 200
4(2b-5) + 3b = 200
8b – 20 + 3b = 200
11b – 20 = 200
11b = 220 b = 20, a = 2(20) – 5 = 35
(35,20)       4(35) + 3(20) = 200 140 + 60 =200
page 199
A shipment of TV sets contains some weighing
30 kg each and the others weighing 50 kg each.
The total weight of the shipment is 880 kg. If
there are 20 TV sets all together, how many
weigh 50 kg?
Page 200 #1 and # 2
The cost of eight pineapple toppings for frozen
yogurt and three strawberry toppings costs \$22.
Four pineapple toppings and 7 strawberry toppings
also costs \$22. Find the price of each kind of
topping.

Two kinds of candy were combined to make 50
pounds of mixture. The less expensive candy costs
37 cents per pound and the more expensive candy
costs 45 cents per pound. If the total mixture was
worth 40 cents per pound, how many pounds of
each candy were used.
The cost of eight pineapple toppings for frozen yogurt and three strawberry toppings
costs \$22. Four pineapple toppings and 7 strawberry toppings also costs \$22. Find the
price of each kind of topping.

p= cost of pineapple toppings
s = cost of strawberry toppings
8p + 3s = 22
4p + 7s = 22
8p + 3s = 22
-8p – 14s = -44
- 11s = -22 s = 2
8p + 3(2) = 22 8p = 16 p =2          (2,2)
4(2) + 7(2) = 22 8 + 14 = 22 22=22
Two kinds of candy were combined to make 50 pounds of mixture. The less expensive candy
costs 37 cents per pound and the more expensive candy costs 45 cents per pound. If the total
mixture was worth 40 cents per pound, how many pounds of each candy were used.

x = number of pounds of 37 cent candy
y = number of pounds of 45 cent candy
x + y = 50     (total number of pounds)
.37x + .45y = .40(50) (total cost of mixture)
37x + 45y = 2000 ( multiply by 100 to eliminate decimal)
-37x – 37y = -1850 (multiply 1st equation by -37)
8y = 150 y=18.75
x + 18.75 = 50 x =31.25 (31.25, 18.75)
.37(31.25) + .45(18.75) = 20 11.5625+8.4375 =20
Upstream/Downstream page 201
upstream = against the current  boat goes
slower
downstream = with the current  boat goes
faster
With the wind (tailwind) = plane is pushed by
the wind and goes faster
Against the wind (headwind) = plane flies into
the wind and goes slower
A motorboat traveling with the
current (downstream) can go
100 mile in 4 hours. Against the
current (upstream), it takes 5
hours to go the same distance.
Find the rate of the motorboat
in still water and the rate of the
current.
speed (rate)   time       distance

upstream          x-y              5       100

downstream        x+y              4       100

or define the variables
Let x= speed of boat in still water
Let y = speed of current
5(x-y)=100
4(x+y)=100
solve and check
x-y=20
x+y=25
----------
2x=45
x=22.5
22.5-y=20 y=2.5
(22.5,2.5)
22.5+2.5=25 25=25
The speed of the boat is 22.5 miles per hour
the speed of the current is 2.5 miles
Homework
• Page 202, 204, 205, 206, 207

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