Question

Question

Answer 1

The equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20

From the equation of the linear function given y = mx + b

y indicates the profit earned and x represents the time in hours.

From the question,

After 3 hours, the popcorn stand earned a profit of $25.

∴ The equation becomes $25 = 3m + b ------ (1)

and after 6 hours, the profit was $70.

∴ The equation becomes $70 = 6m + b ------- (2)

Now, we will solve the two equations simultaneously

From the first equation

$25 = 3m + b

We can write that

b = $25 - 3m ------- (3)

Substitute this into the second equation

$70 = 6m + b

We get

$70 = 6m + ($25 - 3m)

$70 = 6m + $25 - 3m

$70 - $25 = 6m - 3m

$45 = 3m

∴ m = $45 ÷ 3

m = $15

Now, substitute the value of m into equation (3)

b = $25 - 3m

b = $25 - 3($15)

b = $25 - $45

b = -$20

∴ m = $15 and b = -$20

Putting these values into the equation y = mx + b we get

y = $15m +(- $20)

∴ y = $15m - $20

Hence, the equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20

Learn more here: brainly.com/question/19511111