Question

Brian started a business selling maps of hiking trails. His initial expense was $200.00. The graph below shows Brian's profit from selling different number of maps. Part C. How much money will brian profit if he sells 300 maps?

Answer 1

Let,

x = Maps sold

y = Profit

a.) Since the graph shows it's linear, let's create an equation applying this formula,

`\text{ y = mx + b}`

From the graph, let's use the ordered pairs (40, 0) and (0, -200) from the given data,

Let's solve for m,

`m\text{ = }\frac{0\text{ - (-200)}}{40\text{ - 0}}\text{ = }(200)/(40)\text{ = 5}`

Let's solve for b, let's use (40,0) for x and y.

`\text{ y = mx + b}`
`0\text{ = (5)(40) + b}`

`\text{ b = -200}`

Thus, the equation will be,

`\text{ y = 5x - 200}`

Or we can rephrase it as an equation to solve for the profit,

`\text{Profit = 5(Maps sold) - 200}`

b.) The ordered pairs (40, 0) and (0, -200) represents Brian's profits from selling a different number of maps.

(40, 0) = Brian will get no profits if he'll only sell 40 maps. His sale will only be just breakeven to his initial expenses.

(0, -200) = Brian will lose $200 which is his initial expense if he couldn't sell a map.

c.) Brian's profit if he sells 300 maps.

Let's use the formula we made from Part. a,

`\text{ y = 5x - 200}`

x = 300, we get,

`\text{ y = 5(300) - 200 = 1500 - 200 = 1300 = \$1,300}`

Brian will earn $1,300 dollars if he sells 300 maps.