Solving by Graphing
y = x + 4
y = 2x + 5
r + s = -6
r - s = -10
x = 4y
2x + 3y = 22
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. How many hot dogs were sold and how many sodas were sold?
(35, 52): 35 hot dogs and 52 sodas.
y = 3x - 2
y = -x - 2
8a + 5b = 9
2a - 5b = -4
y = x - 2
3x - y = 16
A college student bought 6 shirts and a tank of gas for $200. A week later, at the same prices, he bought 9 shirts and another tank of gas for $281. What was the cost of one shirt? How much for a tank of gas?
(27, 38): One shirt costs $27 and a tank of gas costs $38.
y = -3
x = 5
2x + 3y = 6
3x + 5y = 15
y = 3x - 1
7x + 2y = 37
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
(400, 200): 400 advanced tickets, 200 game-day tickets
y = (1/3)x - 3
2x - y = 8
2a - 4b = 12
-8a + 16b = -48
3s - 2t = 4
t = 2s - 1
You want to put a garden in your backyard. After some research, you find that the ideal garden should be rectangular. The length of this garden is equal to triple the width of it. What is the length and width of this garden if you only have enough space for a garden whose perimeter is 88 feet?
Length = 33 feet
Width = 11 feet
y - 3x = 3
y = 3x - 2
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
t + u = 12
t = (1/3)u
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. What is t, the cost of a taco, and m, the cost of a small glass of milk?
(1.15, 0.95): A taco costs $1.15 and a small glass of milk costs $0.95.