ASL
Suppose you are on the junior class prom committee. You are selling boxes of candy to raise money for a dance hall. There are two box sizes. One box cost $2.00 and the other cost $5.00. Your committee sold 500 boxes. You raised $1450. How many boxes were sold for $2.00 and how many were sold for $5.00?
ASL
How would you solve this problem? A lot of people would guess and check until they came up with the correct answer. One way to solve this problem is by graphing.
ASL
First, think about what the problem is asking you: How many boxes were sold for $2.00 and how many were sold for $5.00? Because we are looking for two values, we have two unknowns, x and y. Let x represent the number of boxes sold for $2.00, and y represent the number of boxes sold for $5.00.
ASL
What do we know about x and y? We know that x + y = 500, and that $2.00x+$5.00y=$1450. If we graph these two equations on the same coordinate plane will we find our answer to how many boxes were sold for $2.00 and how many were sold for $5.00?
ASL
Graph the two lines on the same coordinate plane finding the point of intersection. The point where the two lines intersect is your answer. What is the point of intersection? (350, 150). There were 350 boxes of candy sold for $2.00 and 150 boxes of candy sold for $5.00.
ASL
Put your equations in the systems of equations calculator,or the slope form calculator.
ASL
Now let us try another example:
ASL
You are starting a bumper sticker business. The start up cost is $150.00. Each bumper sticker cost $3.00 to make. You are selling each bumper sticker for $5.00. How many bumper stickers must you sell in order to break even?
ASL
To break even means this is the point where the income is equal to the cost. How many would you need to sell to make a $200 profit? Let us work out this problem.
ASL
The cost of making x bumper sticker is represented by: y = 150 + 3x
The income from x bumper stickers is represented by: y = 5x
ASL
By putting these two equations in the systems of equations calculator,or the slope form calculator, we will find the point where you will "break even." These equations are written in slope intercept form. You should use the calculator that fits this form of equation. The point of intersection is (75,375). That means that you need to sell 75 bumper stickers and make $375 in order to "break even".
ASL
In order to make a $200.00 profit, we have to change your equations. The first equation becomes y = 350 + 3x. The 150 changed to 350 because we added a $200 profit. The second equation remains the same because we didn't change the price of the bumper stickers. By putting these two equations into the systems of equations calculator,or the slope form calculator.we will find how many bumper stickers you must sell in order to make a $200.00 profit.
ASL
y = 350 + 3x
= 5x
ASL
The point of intersection is (175,875). This means you will need to sell 175 bumper stickers and make $875 in order to make a $200 profit.
ASL
Let's try this one:
ASL
You are renting a 15-passenger van for the day after graduation trip to the beach. One company chargers $55.49 a day plus $.25 each mile and another company charges $71.30 a day plus $.07 a mile. You need to determine which company would best serve your needs in each of these different situations.
ASL
A. You are going to a beach 80 miles away.
B. You are going to a beach 50 miles away and are staying 2 days.;
C. You are going to tour a major city 75 miles away and the tour is 15 miles.
ASL
Check your answers using the systems of equations calculator,or the slope form calculator.
