# Applications involving Systems of Equations

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Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to apply systems of linear equations.

Applications Involving Systems of Equations
Examples:
1. Find the two numbers for which the sum is 93 and the difference is 9.
2. The perimeter of a rectangle is 160 yd. The width is 4 more than 1/2 the length. Find the length and the width.
3. Sunset rents a 18 ft truck for \$49.95 plus 75 cents per mile. Cactus rebts a 18 ft van for \$59.95 plus 50 cents per mile. For what mileage is the cost the same?

More Applications Involving Systems of Equations
Examples:
1. Assume all Phoenix College courses are worth either 3 or 4 credits. The cross country team is taking a total of 40 courses that are worth 144 credits. How many 3-credit courses and how many 4-credit courses are being taken?
2. Hoe Mart charges \$3.50 for a CFL light bulb and Supply Depot charges \$2.50 for a CFL light bulb that doesn't last quite as long. If your apartment complex lost the invoice, but knew they purchased 300 bulbs and spent \$885, how many bulbs were purchased from each store?
3. Ground Works charges \$8.00/lb for premium roast coffee and \$4.50/lb for value roast coffee. How much of each type should be used to make a 10 lb blend that would cost \$5.90/lb?
4. A train leaves Prescott, AZ and travels north to the Grand Canyon at a speed of 25 mph. One and a half hour later, an express train leaves on a parallel track and travels north at 60 mph. How far from the starting station will they meet?

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