3-4 Problem Solving Using a System of Equations
PreAP Algebra IIName______
3-4 Problem Solving Using a System of EquationsDate______Period______
Set up a system of equations and solve algebraically.
1.The sum of a certain number and a second number is -42. The first number minus the second is 52. Find the numbers.
2.The difference between two numbers is 16. Three times the larger number is nine times the smaller. What are the numbers?
3.Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed together to get a 350-lb mixture that is 12% protein?
4.One canned juice drink is 15% orange juice and another is 5% orange juice. How many liters of each should be mixed together to get a 10 L solution that is 10% orange juice?
5.Two investments were made totaling $8,800. For a certain year these investments yielded $1326 in simple interest. Part of the $8,800 was invested at 14% and part at 16%. Find the amount invested at each rate.
6.A total of $1150 was invested, part of it at 12% and part at 11%. The total yield was $133.75. How much was invested at each rate?
7.A train leaves a station and travel north at 75km/h. Two hours later, a second train leaves on a parallel track and travels north at 125 km/h. How far from the station will they meet?
8.Two motorcycles travel toward each other from Chicago and Indianapolis, which are about 350 km apart, at rates of 110 and 90 km/h. They started at the same time. In how many hours will they meet?
9.One day a store sold 30 sweatshirts. White ones cost $9.95, and yellow ones cost $10.50. If $310.60 worth of sweatshirts were sold,how many of each color were sold?
10.One day a store sold 45 pens, one kind at $8.50 and another kind at $9.75. In all $398.75 was taken in. How many of each kind of pens were sold?
11.Carlos is 8 years older than his sister Maria. Four years ago Maria was two thirds as old as Carlos. How old are they now?
12.The perimeter of a rectangular field is 628 m. The length of the field exceeds its width by 6 m. Find the dimensions.
13.The perimeter of a rectangle is 86 cm. The length is 19 cm greater than the width. Find the length and the width.
14.Mr. Irwin and Mr. Lippi are mathematics teachers. They have a total of 46 years of teaching. Two years ago Mr. Irwin had taught 2.5 times as many years a Mr. Lippi. How long has each taught?
15.The tens digit of a two digit positive integer is 2 more than three times the ones digit. If the digits are interchanged, the new number is 13 less than half the given number. Find the given integer. (Hint: Let x = tens-place digit and y = ones-place digit, then 10x + y is the number.)
16.The measure of one of two supplementary angles is 8 degrees more than three times the other. Find the measure of the larger of the two angles.
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