Real World 1. At a Boy Scout fund-raising dinner, Mr. Jones bought 2 adult meals and 3 child meals for $23. Mrs. Gomez bought 4 adult meals and 2 child meals for $34. Write a system of linear equations to represent this information and then solve the system to find the cost of one adult meal and one child meal. 2. The costs for tickets to see a play are $15 for adults and $12 for students. A group of 11 adults and students bought tickets for the play. If the total cost was $156, how many of each type of tickets did they buy? 3. Ace Car Rental rents a car for $45 a day and $0.25 per mile. Star Car Rental rents a car for $35 per day and $0.30 per mile. How many miles would a driver need to drive before the cost of renting a car at both rental agencies are the same?
4. The charge for admission to the zoo is $3.25 for each adult and $1.50 for each child. On a day when 500 people paid to visit the zoo, the receipts totaled $1275. Find the number of adult tickets purchased that day.5. The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.6. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 busses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students as did the buses. Find the number of students in each van and each bus.
Coin 7. Linda has 20 coins in her pocket. Some of them are nickels and the rest are dimes. The value of nickels and dimes together is $1.40. How many dimes does Linda have? 8. The number of quarters that Eleanor has is 3 times the number of nickels. She has $1.60 in all. How many of each coins of each type does she have? 9. You have a total of 21 coins, all nickels and dimes. The total value is $1.70. How many nickels and dimes do you have?
10. Greg has 20 coins in his pocket consisting of quarters and pennies. The total value of $1.88. How many quarters and pennies do you have?11. Frances has a total of 27 coins in her purse consisting of nickels and pennies. The coins have a total value of $0.63. How many nickels and pennies does she have?12. Brent is cashing in his piggy bank. It consists of a total of 81 coins that are quarters and dimes. He receives $11.55 for the coins. How many quarters and dimes does Brent have.
Digit 13. The sum of two numbers is 24. One number is three times the other number. What are the two numbers? 14. The sum of two numbers is 34. The difference of the two numbers is 14. Find each of the numbers 15. The sum of two numbers is 45. One number is four times the other. What are the two numbers?
16. Find the value of two numbers if their sum is 12 and their difference is 4.17. The difference of two numbers is 3. Their sum is 13. Find the numbers.18. The sum of two numbers is 41. Their difference 11. Find the numbers.
Break Even 19. A local band is planning to make a compact disc. It will cost $12,000 to record and produce a master copy, and an additional $2.50 to make each sale copy of the disc. If they plan to sell the final product for $7.50, how many discs must they sell to break even? 20. McGuffey High School is paying $13,200 for the writing and research of their yearbook, plus a printing fee of $25 per book. If they sell the books for $40 each, how many will they have to sell to break even? 21. Jared has volunteered 50 hours and plans to continue volunteering 3 hours per week. Clementine just started volunteering 5 hours per week. Find the number of weeks in which Jared and Clementine will have both volunteered the same number of hours.
Wind/Current 22. Flying to Madagascar with a tailwind a plane averaged 158 km/hr. On the return trip, the plane only averaged 112 km/hr while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air 23. Paddling in a canoe to a campsite against the current, you travel at 3.5 mph. On the return trip (with current) you paddle at 5.7 mph. What is the speed of the canoe in still water? What is the speed of the current? 24. Rose took a half hour to row 3 km with the current. When she returned, she took an hour and a half. Find her rowing rate and the speed of the current.
25. With a tail wind, a light plane can fly 375 km in 1 hour. Going against the wind, the plane can fly 290 km/h. What are the speeds of the wind and the plane?26. On a canoe trip, Rita paddled upstream (against the current) at anaverage speed of 2 mi/h relative to the riverbank. On the return tripdownstream (with the current), her average speed was 3 mi/h. FindRita’s paddling speed in still water and the speed of the river’s current.27. A light plane flew from its home base to an airport 255 miles away.With a head wind, the trip took 1.7 hours.The return trip with a tailwind took 1.5 hours. Find the average airspeed of the plane and theaverage windspeed. (HINT: rate*time = distance)
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