5.4B CW Applying Systems of Linear Equations
PowerPoint
Alg 1H
Define two variables. Write 2 equations. State the best method for solving.
1.
The length of a rectangle is 2m more than twice the width. The perimeter is 82m. Find the
dimensions of the rectangle.
2.
The eighth grade class at LCMS has 335 students. Twice the number of girls is equal to three
times the number of boys. How many boys and how many girls are in the class?
3.
The cost of 3 boxes of envelopes and 4 boxes of note paper is $13.25. Two boxes of envelopes
and 6 boxes of note paper cost $17. Find the cost of each box of envelopes and each box of
note paper.
4.
Twenty pounds of dried fruit mix contained prunes worth $2.90 a pound and apricots worth $3.15
a pound. How many pounds of each did the mix contain if the total value of the mix was $59.75?
5.
Mr. Scott had part of his $5000 savings in an account that earned 8% interest and the rest in an
account that earned 12% interest. How much did he have in each account if his annual interest
income from the total investment was $514.80?
6.
The sum of two numbers is 100. Five times the smaller number is 8 more than the larger
number. What are the two numbers?
5.4B HW
Using Systems of Equations to Solve Word Problems
Alg 1H
ALL WORK IS TO BE SHOWN NEATLY ON BINDER PAPER. Label your variables, write a system of
equations, solve the system using either substitution or linear combinations; then answer the problem.
Remember word problems need word answers.
1.
Two cars traveled in opposite directions from the same starting point. The rate of one car was 20
km/h less than the rate of the other car. After 5 hours, the cars were 700 km apart. Find the rate of each
car.
2.
The length of a rectangle is 7 cm more than the width. The perimeter is 78 cm. Find the
rectangle’s dimensions.
3.
A shopper paid $7.70 for 2 containers of milk and 3 containers of apple juice. It would have cost
60 cents more for 2 containers of apple juice and 3 containers of milk. How much would it cost to buy
one container of each?
4.
How many kilograms of nuts worth $5 per kilogram should be mixed with 6 kg. of nuts worth $9
per kilogram to make a mix worth $6.50 per kilogram?
5.
Lizzie Borden receives an annual income of $277 from investing one amount of money at 6% and
another amount at 8%. If the investments were interchanged, her income would increase by $6. Find
the amount she has invested at 8%.
6.
JoAnn’s income from two stocks last year was $620. One stock pays dividends at the rate of 7%
and the other stock at the rate of 9%. If she has invested a total of $8000, how much is invested at
7%?
7.
This year, the total number of dogs and cats sold by the Animal Adoption Agency was 1216. Last
year, 420 more cats and double the number of dogs were sold for a total of 2024. How many of each
were sold this year?
Optional Challenge Problem
In 1943, the Brooklyn Bridge was 10 times as old as the Golden Gate Bridge. That same year,
the difference in their ages was 54 years. Find the year of completion for each bridge.
5-A8 Chemical Mixture Word Problems (PowerPoint)
Alg 1H
Ex. 1: Mrs. Armstrong has 40 ml of a solution that is 50% acid. How much water should she add to make
a solution that is 10% acid?
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Ex. 2: How many liters of water must Mr. Wade EVAPORATE from 50 L of a 10% salt solution to
produce a 20% salt solution?
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Ex. 3: Milk with 3% butterfat was mixed with cream with 27% butterfat to produce 36 L of Half-and-Half
with 11% butterfat content. How much of each was used?
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Ex. 4: A chemistry experiment calls for a 30% solution of copper sulfate. Mrs. Maiorca has 40 milliliters
of 25% solution. How many milliliters of 60% solution should she add to make a 30% solution?
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5-A8 HW Using Systems of Equations to Solve Word Problems
Alg 1H
ALL WORK IS TO BE SHOWN NEATLY ON BINDER PAPER. Label your variables, write a system of
equations, solve the system using either substitution or linear combinations, then answer the problem.
Remember word problems need word answers.
1.
If 800 ml of a juice drink is 15% grape juice, how much pure grape juice should be added to make a
drink that is 20% grape juice?
2.
How many liters of water must be evaporated from 20L of a 30% salt solution to produce a 50%
solution?
3.
The following milk products contain the following amounts of butterfat: 1% milk is 1% butterfat,
cream is 9% butterfat, and whole milk is 4% butterfat. How many ounces of 1% milk and cream
would you have to mix together to make a gallon (128 ounces) of whole milk?
4.
How many milliliters of water must be added to 60ml of a 15% iodine solution in order to dilute it to
a 10% solution?
5.
How many liters of water must be evaporated from 84 L of a 5% salt solution to produce a solution
that is 35% salt?
6.
Wild rice sells for $6 per pound, and plain rice sells for $1 per pound. A grocer wants 10 pounds of
a mixture to sell for $2 per pound. How much of each type of rice must be used?
7.
How many liters of pure antifreeze must be added to 30 L of a 60% antifreeze solution to obtain a
75% solution?
8.
How many liters of water must be evaporated from 80 L of a 20% salt solution to produce a 25%
salt solution?
9.
How many liters of a 30% acid solution must be added to 80 L of a 20% solution to produce a 28%
acid solution?
10.
One type of antifreeze is 40% glycol, and another type of antifreeze is 60% glycol. How much of
each kind of antifreeze should be mixed to make 100 gallons of antifreeze that is 48% glycol?
5-A9 CW Wind and Current Problems (PowerPoint)
Alg 1H
Ex. 1: Mr. Klinger went 27 miles downstream in a boat in three hours. The return trip upstream
took three times as long (nine hours). Find the rate of the boat in still water and the rate of the
current.
Ex. 2: Mrs. Logan took 5 hours to row 60 km downstream and 4 hours to row 40 km upstream.
Find the rate of the boat in still water and the rate of the current.
Ex. 3: Mrs. Greenberg can swim 4 km with the current in 24 minutes. The same distance would
take her 40 minutes against the current. Find the rate of the current and Mrs. Greenberg’s
speed.
Ex. 4: Flying into the wind, Mr. Wutkee flew 2800 km in 3.5 hours. The return trip, flying with the
wind, took 2.5 hours. Find the rate of his plane in still air and the rate of the wind.
5-A9 HW Using Systems of Equations to Solve Word Problems
Alg 1H
ALL WORK IS TO BE SHOWN NEATLY ON BINDER PAPER. Label your variables, write a
system of equations, solve the system using either substitution or linear combinations, then
answer the problem. Remember word problems need word answers.
1.
A plane goes 2000 miles in five hours flying against the wind. The same plane takes four
hours to fly the same distance with the wind. What’s the rate of the plane in still air, and
the rate of the air current?
2.
A man took three hours to go 24 miles downstream, and six hours to return the 24
miles upstream. What was the rate of the boat in still water and the rate of the
current?
3.
Flying with the wind, wonder Woman flew her aircraft 300 miles in five hours. To return the
300 miles, she took six hours, flying against the wind. What was the rate of the superplane
in still air and the rate of the air current?
4.
A woman took three hours to go 48 miles downstream, and six hours to return upstream
all 48 miles. What was the rate of the boat in still water and the rate of the current?
5.
A small plane can fly 2400 km in 10 hours flying into the wind. With the wind behind it, the
plane can fly 3200 km in the same time. What is the speed of the wind?
6.
Alice cycles to Carla’s house at 12 mph and returns by car at 36 mph. If the round trip
takes 1 hour, how far from Carla does Alice live?
7.
Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes
riding against the wind. What was the speed of the wind in miles per hour?
8.
Meg is 20 years younger than Phillip. In three years Phillip will be twice as old as Meg will
be. How is each now?
9.
Flying against the wind, Mr. Trump’s company plane flew 450 miles from one airport to
another in 1½ hours. The return trip, with no change in the wind’s speed or direction, took
1 ¼ hours. What was the speed of the wind?
10.
Two cars pass Exit 20 on the turnpike at 8:00 A.M. One car is traveling north and the
other is traveling south at a speed that is 4 km/h faster than the northbound car. At 8:45
A.M. the cars are 117 km apart. Find the speed of the southbound car.