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
Answer:
3.
Step-by-step explanation:
Remark
There is no short way to do this problem and no obvious way to get the answer other that to solve each part.
Solve
A
Multiply by 2
x + 1.6 = 2(x + 0.1) Remove the brackets
x + 1.6 = 2x + 0.1*2
x + 1.6 = 2x + 0.2 Subtract x from both sides
1.6 = x + 0.2 Subtract 0.2 from both sides
1.6 - 0.2 = x
1.4 = x
Circle A
B
Subtract 2x from both sides.
3x - 2x = 1.4
Circle B
C
Remove the brackets.
4x + 6 = 2x - 6 Add 6 to both sides
4x + 12 = 2x Subtract 4x from both sides.
12 = -2x Divide by - 2
12/-2 = x
x = - 6 Don't circle C
D
I'm going to be very scant in my solution of this. You can fill in the steps.
3x = 4.2
x = 4.2/3
x = 1.4
Circle D
Answer:
$56
Step-by-step explanation:
Answer:
0.08
Step-by-step explanation:
