Word Problems

Solving Methods Graphing Substitution Elimination

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Word Problems

1) You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell?

Define variables:

 

System of equations:

State your solution(s):

Solve

X = student ticketsY = Adult tickets

x + y = 3503x + 5y = 1450

x + y = 350 3x + 5y = 1450

y = 350 – x

3x + 5(350 – x) = 1450

3x + 1750 – 5x = 1450

1750 – 2x = 1450

– 2x = -300

x = 150

x + y = 350

150 + y = 350

y = 200

(150, 200)

We sold 150 Student tickets and 200 adult tickets

Word Problems

2) Missy Elliot loves to shop at Neiman Marcus. Last Saturday she bought pants and shirts for her new video. Each shirt cost $125 and each pair of pants cost $225. She came home with 26 items and spent exactly $4950. How many pants and shirts did Missy buy?

Define variables:

 

System of equations:

State your solution(s):

Solve

X = pantsY = Shirts

X + y = 26125x + 225y = 4950

x + y = 26

y = 26 – x

125x + 225(26 – x) = 4950

125x + 5850 – 225x = 4950

5850 – 100x = 4950

– 100x = -900

x = 9x + y = 26

9 + y =26

y = 17

(9, 17)

Missy bought 9 pants and 17 shirts

Word Problems

3) You are in charge of decorating the gym for the Homecoming dance. You purchased 6 bags of balloons and 5 bags of large sparkling hanging stars all for $19.20. You soon realized that this was not enough to decorate the entire gym. On your second trip to the store, you bought 8 bags of balloons and 2 bags of large sparkling hanging stars all for $15.80. What was the price for each item?

Define variables:

 

System of equations:

State your solution(s):

Solve

X = balloonsY = sparkling hangers

6x + 5y = 19.508x + 2y = 15.80

6x + 5y = 19.50y = -1.2x + 3.9

8x + 2y = 15.80y = -4x + 7.9

-4x + 7.9 = -1.2x + 3.9

-4x + 4 = -1.2x

4 = 2.8x

1.43 = x

y = -4x + 7.9y = -4(1.43) + 7.9

y = 2.19

The Balloons cost $1.43 and the Sparkling hangers cost $2.19

Word Problems

4) K-Mart had a sale on DVD’s and video tapes for Labor Day weekend. Katie bought 2 tapes and 3 DVD’s and spent $134. Emily bought 1 tape and 5 DVD’s and spent $179. How much does each tape and DVD cost?

Define variables:

 

System of equations:

State your solution(s):

Solve

X = dvdsY = video tapes

3x + 2y = 1345x + 1y = 179

DVDs cost $32 and each video tape is $19

3x + 2y = 134-10x + -2y = -358

-2 ( )

-7x = -224 x = 32

3x + 2y = 1343(32) + 2y = 134

96 + 2y = 134

2y = 38

y = 19

Word Problems

5) Wes Plumbing charges a $35 base rate and $75 per hour. Elk Plumbing charges a $50 base rate and $60 per hour. At what time (in hours), will the charge for Wes Plumbing and Elk Plumbing be the same?

Define variables:

 

System of equations:

State your solution(s):

Solve

X = hours workedY = total cost

Y= 75x + 35Y= 60x + 50

Y= 75x + 35Y= 60x + 50

75x + 35 = 60x + 50

75x = 60x + 15

15x = 15x = 1

Y= 75(1) + 35

Y= 110At 1 hour worked both companies charge the same amount.