Applications of Systems of Equations

Three Steps to solving applications

- Step 1 NAME YOUR VARIABLES!! What are you

looking for and what are you going to call them

in math language? - Step 2 Write the number of equations that

equals the number of variables. - Step 3 Line up variables and solve using

matrices OR solve for y and graph.

Example 1

- You are selling tickets at a high school football

game. Student tickets cost 2, and general

admission tickets cost 3. You sell 1957 tickets

and collect 5035. How many of each type of

ticket did you sell?

YOU DO 1 Which of the following would be your

variables?

- x of 3 point questions
- y amount of money
- x total of questions
- y of 5 point questions

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You Do 1 Which of the following equations

would you use to solve the problem?

- x y 150
- x y 46
- 5x 3y 150
- 3x 5y 150

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What is the solution to YOU DO 1

- 5 3pt questions and 3 5pt questions
- 196 3pt questions and 888 5pt questions
- 40 3pt questions and 6 5pt questions
- 6 3pt questions and 40 5pt questions

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Example 2

- A collection of nickels and dimes is worth 3.30.

There are 42 coins in all. How many of each

coin are there?

YOU DO 2 Which of the following would be your

variables?

- x of coins
- y amount of money
- x of dimes
- y of quarters

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You Do 2 Which of the following equations

would you use to solve the problem?

- x y 100
- x y 21.40
- 10x 25y 21.40
- .10x .25y 21.40

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What is the solution to YOU DO 2

- 76 quarters and 24 dimes
- 24 dimes and 76 quarters
- 165 dimes and -65 quarters
- 121 dimes and 15 quarters

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Example 3

- The perimeter of a lot is 84 feet. The length

exceeds the width by 16 feet. Find the length

and width of the lot.

YOU DO 3 Which of the following would be your

variables?

- x perimeter
- y width
- x length
- y dimensions

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You Do 3 Which of the following equations

would you use to solve the problem?

- x y 42
- 2x 2y 42
- x y 4
- y x 4

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What is the solution to YOU DO 3

- 12.5 ft long X 8.5 ft wide
- 23 ft long X 19 ft wide
- 12.5 ft wide X 8.5 ft long
- 23 ft wide X 23 ft long

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Example 4

- Three solutions contain a certain acid. The

first contains 10 acid, the second 30, and the

third 50. A chemist wishes to use all three

solutions to obtain a 50 liter mixture

containing 32 acid. If the chemist wants to use

twice as much of the 50 solution as the 30

solution, how many liters of each solution should

be used?

YOU DO 4 Which of the following would be your

variables?

- x amount 40 solution
- y of liters
- x of batches
- y amount of 60 solution

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You Do 4 Which of the following equations

would you use to solve the problem?

- x y 8
- .4x .6y 4.4
- x y 55
- .4x .6y .55

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What is the solution to YOU DO 4

- 6 liters of the 40 solution and 4 liters of the

60 solution - 21.25 liters of the 40 solution and 13.25 liters

of the 60 solution - 2 liters of the 60 solution and 6 liters of the

40 solution - 2 liters of the 40 solution and 6 liters of the

60 solution

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Example 5

- The sum of two numbers is -11. Twice the first

number minus the second is 32. Find the numbers.

YOU DO 5 Which of the following would be your

variables?

- x first integer
- y second integer
- x sum of integers
- y difference of integers

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You Do 5 Which of the following equations

would you use to solve the problem?

- x y 12
- x y 12
- x y 38
- x y 38

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What is the solution to YOU DO 5

- The first integer is 13 and the second integer is

25 - The first integer is 38 and the second integer is

12 - The first integer is 25 and the second integer is

13 - The first integer is 26 and the second integer is

14

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White board practice!

Carla bought 3 shirts, 4 pairs of pants, and 2

pairs of shoes for a total of 149.79. Beth

bought 5 shirts, 3 pairs of pants, and 3 pairs of

shoes for 183.19. Kayla bought 6 shirts, 5

pairs of pants, and a pair of shoes for 181.14.

Assume that all of the shirts were the same

price, all of the pants were the same price, and

all of the shoes were the same price. What was

the price of each item? Step one What are your

variables?

- x of shirts
- y of pairs of pants
- z of pairs of shoes
- x price of a shirt
- y price of a pair of pants
- z price of a pair of shoes

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Carla bought 3 shirts, 4 pairs of pants, and 2

pairs of shoes for a total of 149.79. Beth

bought 5 shirts, 3 pairs of pants, and 3 pairs of

shoes for 183.19. Kayla bought 6 shirts, 5

pairs of pants, and a pair of shoes for 181.14.

Assume that all of the shirts were the same

price, all of the pants were the same price, and

all of the shoes were the same price. What was

the price of each item? Step two What are your

equations?

- x y z 149.79
- 3x 4y 2z 149.79
- 5x 3y 3z 183.19
- 3x 5y 6z 149.79
- 14x 12y 6z 181.14
- 6x 5y z 181.14

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Carla bought 3 shirts, 4 pairs of pants, and 2

pairs of shoes for a total of 149.79. Beth

bought 5 shirts, 3 pairs of pants, and 3 pairs of

shoes for 183.19. Kayla bought 6 shirts, 5

pairs of pants, and a pair of shoes for 181.14.

Assume that all of the shirts were the same

price, all of the pants were the same price, and

all of the shoes were the same price. What was

the price of each item? Step three Find the

price of each item. (Click in your answer for the

price of a pair of shoes)

- 23.49
- 0

Tristen is training for his pilots license.

Flight instruction cost 105 per hour, and the

simulator costs 45 per hour. The school

requires students to spend 4 more hours in

airplane training than in the simulator. If

Tristen can afford to spend 3870 on training,

how many hours can he spend training in an

airplane and in a simulator? Step one What

are the variables of this problem?

- x cost of flying an airplane
- x of hours in airplane.
- y of hours in the simulator
- Y cost of flying in the simulator

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Tristen is training for his pilots license.

Flight instruction cost 105 per hour, and the

simulator costs 45 per hour. The school

requires students to spend 4 more hours in

airplane training than in the simulator. If

Tristen can afford to spend 3870 on training,

how many hours can he spend training in an

airplane and in a simulator. Step 2 What

equations can be used to solve this problem?

- x y 3870
- 150x 45y 3870
- x y 4
- y x 4

Default MC Any MC All

Tristen is training for his pilots license.

Flight instruction cost 105 per hour, and the

simulator costs 45 per hour. The school

requires students to spend 4 more hours in

airplane training than in the simulator. If

Tristen can afford to spend 3870 on training,

how many hours can he spend training in an

airplane. Step 3 Solve the problem using any

method.

- 27
- 0.0

Valery is preparing an acid solution. She needs

200 milliliters of 48 concentration solution.

Valery has 60 and 40 concentration solutions in

her lab. How many milliliters of 40 acid

solution should be mixed with 60 acid solution

to make the required amount 48 acid solution?

Step one Name the variables

- x amount of 60 solution
- y amount of 48 solution
- y amount of 40 solution
- x amount of 200 milliliter solution

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Valery is preparing an acid solution. She needs

200 milliliters of 48 concentration solution.

Valery has 60 and 40 concentration solutions in

her lab. How many milliliters of 40 acid

solution should be mixed with 60 acid solution

to make the required amount 48 acid solution?

Step two Write the equations

- x y .48(200)
- .4x .6y .48(200)
- .6x .4y .48(200)
- x y 200

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Valery is preparing an acid solution. She needs

200 milliliters of 48 concentration solution.

Valery has 60 and 40 concentration solutions in

her lab. How many milliliters of 40 acid

solution should be mixed with 60 acid solution

to make the required amount 48 acid solution?

Step 3 Solve using matrices.

- 120
- 0.0

Jambalaya is a Cajun dish made from chicken,

sausage, and rice. Simone is making a large pot

of jambalaya for a party. Chicken cost 6 per

pound, sausage cost 3 per pound, and rice costs

1 per pound. She spends 42 on 13 and a half

pounds of food. She buys twice as much rice as

sausage. How much sausage will she use in her

dish. Step one Name your variables

- x cost of the chicken
- y cost of the sausage
- z cost of the rice
- x amount of chicken
- y amount of sausage
- z amount of rice

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Jambalaya is a Cajun dish made from chicken,

sausage, and rice. Simone is making a large pot

of jambalaya for a party. Chicken cost 6 per

pound, sausage cost 3 per pound, and rice costs

1 per pound. She spends 42 on 13 and a half

pounds of food. She buys twice as much rice as

sausage. How much sausage will she use in her

dish. Step two Make your equations.

- x y z 42
- x y z 13.5
- z 2y
- y 2z
- 6x 3y z 42
- 6x 3y z 13.5

Default MC Any MC All

Jambalaya is a Cajun dish made from chicken,

sausage, and rice. Simone is making a large pot

of jambalaya for a party. Chicken cost 6 per

pound, sausage cost 3 per pound, and rice costs

1 per pound. She spends 42 on 13 and a half

pounds of food. She buys twice as much rice as

sausage. How much sausage will she use in her

dish. Step three solve.

- 3
- 0.0

Devonte loves the lunch combinations at Rositas

Mexican Restaurant. Today however, she wants a

different combination than the ones listed on the

menu.

- Lunch Combo Meals
- Two Tacos, One Burrito ..6.55
- One Enchilada, One Taco, One Burritio..

7.10 - Two Enchiladas,
- Two Tacos.8.90

- 7.80
- 0.0

If Devonte wants to make a combo of 2 burritos

and 1 enchilada, how much should he plan to spend?

The sum of 3 numbers is 20. The second number is

4 times the first, and the sum of the first and

third is 8. Find the numbers.

- 3
- 15
- 12
- 5

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