Question 998997: Last year, Carrie made $54,785 with her massage therapy business, with $22,300 in expenses. This year she's anticipating $24,030 in expenses. How much revenue will she need to bring to guarantee that her business is growing?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! assuming that her revenue to expense ratio will remain the same, then set up a ratio and solve for the value of the required revenue next year.
your ratio is:
54,785 / 22,300 = x / 24,030
54... is this year's revenue.
22... is this year's expenses.
x is next year's revenue.
24... is next year's expenses.
you want to solve for x.
cross multiply to get:
54,785 * 24,030 = x * 22,300.
divide both side s of this equation by 22,300 and you get:
x = 54,785 * 24,030 / 22,300
solve for x to get:
x = 59,035.14
she would have to take in at least that much to show that her business is growing, assuming that her revenue to expense ratio remains the same.
this is a big assumption, and it's required in order for these ratio formulas to work on a problem such as this.
you can also look at this as a direct variation type problem.
y = k*x.
first you solve for k using this year's figures.
y = 54,785
x = 22,300
y = k*x becomes 54,785 = k * 22,300.
divide both sides of this equation by 22,300 and solve for k to get:
k = 54,785/22,300 = 2.456726457.
k is the constant of variation.
now plug in next years' numbers.
revenue = y
k = 2.456726457
x = 24,030
y = k * x becomes y = 2.456726457 * 24,030.
this results in:
y = 59,035.14
same answer, as it should be, since both equations solve for a direct ratio which can also be modeled as a direct variation.
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