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# sum of taxes

1-3. Set up a system of linear equations to describe the following problem and solve the system using one of the methods discussed this week.
At the end of the year, a business has made a profit of \$151,000. They must calculate the amount of tax due to the federal government and to the state. The federal tax rate is 30%, and the state tax rate is 10%. State taxes (ST) are deductible before federal taxes (FT) are calculated, and federal tax are deductible before states taxes are calculated. In other words, state taxes are subtracted from the profits before the 30% federal tax is calculated, and federal taxes are subtracted from the profits before the 10% state tax is calculated. 10% or 30 % of 151,000 does not require a system of equations to solve. Do not begin in this manner. Create and solve a system of equations to figure out how much state and federal taxes are owed by this company

Cook, B. (2004)and Dugopolski. Math demo class. retrieved March 19, 2004.
1. Identify the variables first. Do not confuse the tax rate with the amount of tax.

2. Set up a system of two equations. This is the only way that this problem can be solved.

3. Solve the system. Remember to report the answer in dollars.

#### Solution Preview

Let P = profits = 151000

let FT = amount of federal tax
let ST = amount of state tax

FT = (P-ST) 0.30 ----this is equation 1
ST = (P-ST-FT) 0.10 ...

#### Solution Summary

The sum of taxes is represented.

\$2.19