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This printable supports Common Core Mathematics Standard HSA-REI.C.6

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# Systems of Equations - Word Problems #2 (Grade 10)

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## Systems of Equations - Word Problems #2

1.
Lincoln High's enrollment decreases at an average rate of 75 students per year, while Erie High's enrollment increases at an average rate of 60 students per year. Lincoln High has 3,150 students enrolled, and Erie High has 2,475 students enrolled. If enrollment continues to change at the same rates, when will the two schools have an equal number of students?

a) Write equations for the model.

b) Solve the equations and answer the question.

2.
There are 200 people attending a banquet. There are 10 less men then there are women. Create a system of linear equations to determine the number of men and women.

3.
The admission at the movies is $5 for children and$10 for adults. The total amount collected was $3000.00. There was a total of 500 people. Create a system of linear equations to figure out how many of the people were children and how many were adults. 4. Two people went shopping for produce. The first person bought 5 pieces of zucchini and 6 avocados for$19.50; the second person bought 8 pieces of zucchini and 3 avocados for $18. What is the cost of each piece of produce? 5. There are 40 animals in a barnyard. Some are cows and some are chickens. One day, farmer Albert goes to the barn and counts 100 legs total. How many of each animal are there? 6. If a man is 3 times older than his son now, and will be 2 times older than his son in 8 years, how old are each now? 7. If chapter 1 in a book contains five more pages than does Chapter 2, and there are 65 total pages in both chapters, how many pages does each chapter contain? 8. If the city plans to plant a total of 18 trees on two streets, putting twice as many trees on Elm Street as on Maple Street, how many trees will be planted on each street? 9. T.J. can type twice as fast as J.R. If they both spend an equal amount of time on a 600-page manuscript, how many pages will they each have typed? 10. A bushel of apples and a bag of flour cost$25. 2 bushels of apples and 3 bags of flour cost \$67.50. Find the cost of a bushel of apples and of a bag of flour.

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