Graphing
y=-8/3x+4
y=-2/3x-2
(3, -4)
Solve by elimination
-4x-4y=4
6x+4y=10
(7, -8)
Solve by graphing
y=3x+4
y=-4x-3
(-1, 1)
Brody starts a car wash business. He invests $1250 to start. The supplies for each car wash cost Brody $1.25 and he charges $7.50 for each. How many cars would have to be washed for Brody to break even?
200 cars would need to be washed for Brody to break even.
Tony is 7 years older than his brother Greg. Three years ago, Greg was one half of Tony's age. Find Greg and Tony's current age.
Tony is 17 and Greg is 10.
4x+3y=-6
x-3y=-9
(-3, 2)
Solve by substitution
4x+8y=-4
x+7y=-21
(7, -4)
Choose any method to solve
-10x+y=-25
20x-7y=25
(3, 5)
During a football game, the parents of the football players sell pretzels and popcorn to raise money for new uniforms. They charge $2.50 for a bag of popcorn and $2 for a pretzel. The parents collect $336 in sales during the game. They sell twice as many bags of popcorn as pretzels. How many bags of popcorn do they sell? How many pretzels do they sell?
They sold 48 pretzels and 96 bags of popcorn.
A movie theater offers a discounted movie pass. The pass costs $25 and each movie costs an additional $6. Seeing a movie without a pass costs $11. After how many movies will it cost the same to be a pass holder as it is to not be a pass holder.
It will cost the same when you have seen 5 movies.
3x+4y=16
3x+4y=8
No solution
Solve by elimination
15x-5y=-5
9x-3y=-3
Infinite number of solutions
Choose any method to solve
-10x-6y=14
y+7=3x
(1, -4)
Jimmy wants to make 13 ml of a 40% solution by mixing a 50% solution and a 37% solution. How much of each solution should he use?
3 ml of the first solution and 10 ml of the second solution.
A boat travels upstream for 4 hours and travels 24 miles. The boat then travels downstream for 3 hours and travels 24 miles. Find the rate of the current and the boat.
Boat: 7 mph
Current: 1 mph
12=-4y+7x
-6y+3x=-12
(4, 4)
Solve by elimination
6x-10y=18
4x-7y=11
(8,3)
A business rents in-line skates and bicycles. A pair of skates rents for $15 per day and a bicycle rents for $20 a day. For one day, the business had a total of 25 rentals and collected $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.
10 Skate rentals and 15 bicycle rentals
Max and Leo left the movie theater at the same time and drove in opposite directions. Leo drove 20 mph faster than Max. After six hours they were 720 miles apart. Find the speed of Leo and Max.
Leo drives at 70 mph and Max drives 50 mph.
Amanda made a trip to target and back. The trip there took 2 hours and the trip back took 5 hours because of a snow storm. Her total trip was 270 miles. She drove 30 mph faster on the trip there than on the trip back. Find Amanda's speed on the trip there and the trip back.
trip there: 60 mph
trip back: 30 mph
-6-2y=x
-x=6+2y
Infinite Number of Solutions
Solve by substitution
-3x+5y=10
2x-5y=-15
(5, 5)
Lily is 2 years younger than Emma. Three times Emma’s age subtracted from five times Lily’s age is Emma’s age. How old are each?
Lily is 8 and Emma is 10.
In your chemistry lab, you have a bottle of 1% hydrochloric acid solution and a bottle of 5% hydrochloric acid solution. You need 100 milliliters of a 3% hydrochloric acid solution for an experiment. How many milliliters of each solution do you need to mix?
50 ml of each solution.
You mix some tea that costs $5.75 per pound with some cheaper tea that costs $1.05 per pound. You obtain 15 pounds of tea that costs $1.50 per pound. How many pounds of each did you use.
tea 1: 2.05 lbs
tea 2: 12.95 lbs