Question

Tim is selling tickets to a school sporting event to raise money for his club. He put some extra money in his box before he began. As he sells tickets, he records the number of tickets he has sold and the total amount of money in the box. Some of his data is shown below:

Number of tickets sold Total money in box(dollars)

7 108.75
13 146.25
18 177.50

Assuming all the tickets are the same price, write an equation that represents the situation above. Explain how to use your equation to determine the amount of money originally in the box before any tickets were sold and the price of each ticket.

Answer 1

The price of each ticket will be the slope found from the data.  

Slope=m=(y2-y1)/(x2-x1)=(177.5-146.25)/(18-13)

m=6.25  (so the cost of the tickets is $6.25)

Now we can use any data point to solve for b, or the y-intercept of the line:

y=6.25x+b, using (177.5, 18)

177.5=6.25(18)+b

b=$65.00d

So he started with $65.00

Answer 2

The equation that represents the situation will therefore be:

y = 6.25x + b

The amount of money that is originally in the box (initial value) is $65.

What is a Linear Equation?

• Where m is the slope/unit rate and b is the y-intercept/initial value, a linear equation can be represented as, y = mx + b.

• Slope (m) = change in y/change in x

To write an equation, first find the slope using any two points, say, (7, 108.75) and (13, 146.25).

Slope (m) = (146.25 - 108.75)/(13 - 7) = 37.5/6 = 6.25

m = 6.25

Substituting m = 6.25 into y = mx + b, the equation that represents the situation will therefore be:

y = 6.25x + b

b represents the initial value, which is the amount of money that is originally in the box.

To find b, substitute (x, y) = (7, 108.75) and m = 6.25 into y = 6.25x + b.

• Thus:

108.75 = 6.25(7) + b

108.75 = 43.75 + b

• Subtract 43.75 from each side

108.75 - 43.75 = b

b = 65

Therefore, the amount of money that is originally in the box (initial value) is $65.

Learn more about linear equation on:

https://brainly.com/question/14294864