By writing the costs as linear equations, we will get:
a) For 3 hours the cost will be the same in both studios.
b) There is no number of hours such that the costs are the same.
After how many hours are the total costs the same at both studios?
The information in the image is the following.
Studio A:
Vase: $10.49
Studio fee: $8 per hour.
So, if you work for x hours in studio A, the total cost will be given by the linear equation:
A(x) = $10.49 + $8*x
For Studio B we have:
Vase: $14.99
Studio fee: $6.50 per hour
Then if you work for x hours in studio B, the cost is:
B(x) = $14.99 + $6.50*x
The cost in the two studios will the same one when:
A(x) = B(x)
Then we need to solve the linear equation:
$10.49 + $8*x = $14.99 + $6.50*x
$8*x - $6.50*x = $14.99 - $10.49
$1.50*x = $4.50
x = $4.50/$1.50 = 3
This means that for a total of 3 hours, the cost in both studios will be the same one.
b) If studio B increases the fee by $1.50, then the linear equation for studio B is:
B(x) = $14.99 + $8*x
Notice that the slope is the same one than in the equation for studio A, this means that the lines are parallel, and thus, the lines never intercept.
So there is no solution to the equation A(x) = B(x), which means that there is no number of hours such that the costs are the same in both studios.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
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