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# Important information About Solving Equations and Word Problems

7(3x+4) = 8(2x+5) + 13

2(x-3) - 3(x+5) = 3(x-2) - 7

3x - 5(3x-7) = 2(x+9) + 45

Geometry: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.

Science and medicine: A bicyclist rode into the country for 5 h. In returning, her speed was 5 mi/h faster and the trip took 4 h. What was her speed each way?

Science and medicine: A bus leaves a station at 1P.M., traveling west at an average rate of 44 mi/h.

Science and medicine: Martina leaves home at 9 A.M., bicycling at a rate of 24 mi/h. To hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?

Business and finance: There are 850 Douglas fir and ponderosa pine trees in a section of forest bought by Sawz Logging Co. The company paid an average of \$300 for each Douglas fir and \$225 for each ponderosa pine. If the company \$217,500 for the trees, how many of each kind did the company buy?

A common mistake when solving equations is the following:
The equation: 2(x-2) = x+3
First step in solving: 2x-2 = x+3
Write a clear explanation of what error has been made. What could be done to avoid this error?

Business and finance: Paul invested \$5000 in a time deposit. What interest will he earn for 1 year if the interest rate is 6.5%?
Science and medicine-A chemist has 300 milliliters (mL) of solution that is 18% acid. How many milliliters of acid are in the solution?

Business and finance: Ms. Jordan has been given a loan of \$2500 for 1 year. If the interest charged is \$275, which is the interest rate on the loan?

Statistics: A survey of 400 people found that 66 were left-handed. What percent of those surveyed were left-handed?
Business and finance-The electricity costs of a business decreased from \$12,000 one year to \$10,920 the next. What is the rate of decrease?

2 times a number, increased by 28, is less than or equal to 6 times that number.

#### Solution Summary

It shows how to set up and solve the equations for the algebra word problem. The solution is detailed and well organized. The response has a '5/5' rating.

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