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y= method
Substitution
Elimination
Matrix
Anything goes
100
y=2x+3 y=3x-2
(5,13)
100
It’s a nice spring day in Alaska. The temperature in Anchorage is -2 times the temperature in Nome. The temperature in Nome is 6 degrees more than -2 times the temperature in Anchorage. What are the temperatures in Nome and Anchorage?
(-2,4)
100
The difference between a blob and a dab is six. The sum of twice a blob and a dab is eighteen. How large is a blob and how large is a dab?
(8,2)
100
Jill has a collection of bugs. Her collection contains butterflies and tarantulas. She has 47 bugs and counts 320 total legs. How many butterflies and how many tarantulas does she have in her collection?
(28,19)
100
A farm has only sheep and geese. It has a total of 58 animals and a total of 180 legs on the animals. How many sheep and geese are on the farm?
(32,26)
200
Joe is looking at a treasure map, which is drawn on a rectangular coordinate grid. However, instead of putting an X where the treasure should be, some sick person left this clue. The treasure is at a spot where one coordinate is the opposite of the other and the y-coordinate is 4 greater than the x- coordinate. At which coordinates should Jose look for the treasure?
(-2,2)
200
At a local bookstore, John purchased a history textbook and a magazine that cost a total of $32, not including tax. If the price of the history textbook, h, is $4 more than 3 times the price of the magazine, m, which system of linear equations could be used to determine the price of the history textbook and the magazine?
(25,7)
200
Sara bought some 6-penny nails and some 10-penny nails at Ace Hardware. She bought 2 more 6-penny nails than she did 10-penny nails. She had a total of 8 nails. How many 6-penny and 10-penny nails did Sara purchase?
(5,3)
200
Coach Barker bought supper for all the participating volleyball players after the tournament. The food was ordered from Fast Food’s to Go, and the choices were hamburger meals for $2.50 or hot dog meals for $1.75. Coach Barker ordered a total of 45 meals and the ticket, not including tax, was $97.50. How many of each meal did she order?
(25,20)
200
Hal and Sal work on a base wage plus commission. Hal makes $150 per week plus a 40% commission on total sales. Sal makes $175 per week plus a 35% commission on total sales. What amount of sales will each need to make their pay equal? What will be their gross pay?
(500,350)
300
Picky Painters charges a flat fee of $300 plus $20 per hour for labor. Color Creators charges a flat fee of $500 plus $12 per hour for labor. After how many hours of labor will the charges for each company be equal? What is the charge?
(25,800)
300
Terence is looking for two numbers. If he multiplies the first number by three and adds one, he gets the second number. However, the first number is only 1/4 of the second number. What are the two numbers?
(1,4)
300
Sam collects insects. However, he only collects ants and beetles. One night while collecting insects for his collection, Sam had an unproductive hunt. The number of ants plus twice the number of beetles was only eight. The difference between the number of ants and beetles was -4. How many ants and how many beetles did he catch?
(0,4)
300
A soccer match was held between Peru and Bolivia with 38,000 in attendance. Adult tickets sold for $8 and children’s tickets sold for $5. Total sales were $257,125. How many of each type of ticket was sold?
(22375,15625)
300
Alexander and his brother Albert work at two different department stores. Alexander is paid a base salary of $250 per week plus a 30% commission on all sales. Albert is paid a base salary of only $125 per week, but gets a 40% commission on all sales.
(1250,625)
400
Airplane at 19,200 feet descending at a rate of 40 feet per second. Another airplane takes off and ascends at a rate of 60 feet per second. After how many seconds will the airplanes be at the same height? What is this height?
(192, 11520)
400
A collection of nickels and quarters is worth $4.65. There are 3 more nickels than quarters. Use a system of equations to determine how many coins are in the collection.
(18,15)
400
I am thinking of two numbers. The sum of two numbers is two. The difference of the two numbers is also two. What are the two numbers?
(2,0)
400
After a baseball game was over the turnstile showed that 1787 people attended. The total cash received for tickets was $5792. Reserved seats cost $4.00 each and general admission cost $3.00 each. Compute the number of each type of ticket sold for the game.
(431, 1356)
400
Gouda cheese and Edam cheese cost different amounts per kilogram. A gift box containing 3 kg of Gouda and 2 kg of Edam costs $24.40. Another gift box containing 4 kg of Gouda and 5 kg of Edam costs $47.70. Assuming the total cost only reflects the cost of the cheeses, what is the price of each cheese per kilogram?
(3.80, 6.50)
500
My brother says that my age is three years less than three-fourths of my dad’s age. My sister says that my age is one year more than three-fourths of my dad’s age. What are my age and my dad’s age?
NO solution
500
Samuel and Eduardo have collected a total of 275 stamps. Samuel has 50 stamps more than twice the number of stamps that Eduardo has. How many stamps does each have?
(75, 200)
500
A truck is carrying 1500 pounds of cargo that occupies 138 cubic feet of space. A television weighs 50 pounds and occupies a space of 4 cubic feet. A microwave oven weighs 30 pounds and occupies a space of 3 cubic feet. How many televisions and microwaves are they carrying.
(12,30)
500
Sweets for the Sweet sells candy in large bins. Each bin normally contains one type of candy, but a customer dumped the gumballs and mega jawbreakers into the same bin. The sales clerk checks the sales records and knows the bin must contain 847 pieces of candy. He weighs the bin and finds it weighs 2851.9 grams. An individual gumball weighs 2.5 grams. An individual jawbreaker weighs 4.2 grams. How many of each type of candy are in the mixed up bin?
(415,432)
500
A beginner’s artist kit costs $6.35 and contains 2 brushes and 5 jars of paint. The standard kit has 4 brushes and 12 jars of paint and costs $13.20.Assuming that all brushes cost the same and that all jars of paint cost the same, what are the prices of a brush and a jar of paint?
(2.55, .25)