His new employer has offered Malcom Davis a choice of profit-sharing plans. For Plan A, he can receive 1/90 of the company’s gross income. For Plan B, he can receive 1/60 of the company’s profit. Gross income is the total amount the company takes in. Profit is the difference of the gross income and expenses. The company’s expenses for one month are $100,000. A) Write an equation for finding the gross income that would give Malcom Davis the same amount of money with either plan.

B) Solve the equation from Exercise A and interpret the solution.

C) How much would Malcom Davis receive when the two plans are the same?

D) If the gross income of the company is less than the amount from Part B, which plan would be better for Malcom Davis? Show work to support your answer.

Malcom Davis earnings is an illustration of equations and proportions.

Let the profit be P, and the gross income be G.

So, we have:

(a) The equations

For plan A, we have:

----1/90 of the company's gross income

For plan B, we have:

 ----1/90 of the company's profit

When both are the same, we have:

This gives

Substitute

Hence, the equation is:

(b) Solve the equation in (a), and intepret

Cross multiply

Collect like terms

Divide both sides by 30

The gross income must be $300000, for Dave to earn the same amount with either plan.

(c) His earnings based on (c)

We have:

Substitute

His earning is $3333.33 when the plans are the same

(d) If the gross income in less than (b)

If the gross income is less than $300,000, then plan A would better for Malcom Davis, because his earnings in plan A would be greater than plan B

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