Systems of Equations

1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot dogs and 4 bags of potato chips for $9.25. Find the cost of each item.


2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult and $12 per senior citizen. If total receipts were $8492, how many senior citizen tickets were sold?


3) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $36.12. The second group bought 6 slices of pizza and 6 soft drinks for $31.74. How much does one slice of pizza cost?


4) Tina Thompson scored 34 points in a recent basketball game without making any 3-point shots. She scored 23 times, making several free

throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2-point field goals did

she make?


5) Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city?


6) A textile company has specific dyeing and drying times for its different cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50 minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing time and 30 minutes of drying time. The production division allocates 2440 minutes of dyeing time and 1680 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried?


7) A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there?


8) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is $1.65 more than the value of the nickels. How many nickels and dimes does Jamil have?


9) A flat rectangular piece of aluminum has a perimeter of 60 inches. The length is 14 inches longer than the width. Find the width.



10) Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 8 feet more than 3 times the width. He needs 64 feet of fencing to do the job. Find the length and width of the garden.


11) Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 18° less than two times the second angle. Find the measure of each angle.


12) The three angles in a triangle always add up to 180°. If one angle in a triangle is 72° and the second is 2 times the third, what are the three angles?


13) An isosceles triangle is one in which two of the sides are congruent. The perimeter of an isosceles triangle is 21 mm. If the length of the congruent sides is 3 times the length of the third side, find the dimensions of the triangle.


14) A chemist needs 130 milliliters of a 57% solution but has only 33% and 85% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.


15) Two lines that are not parallel are shown. Suppose that the measure of angle 1 is (3x + 2y)°, the measure of angle 2 is 9y°, and the measure of

angle 3 is (x + y)°. Find x and y.


16) The manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews for $15 per pound. The manager wishes to make a 35-pound trail mix-cashew mixture that will sell for $14 per

pound. How many pounds of each should be used?


17) A college student earned $7300 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 7% and the rest at 6%. If the student received a total of $458 in interest at the end of the year, how much was invested at 7%?



18) A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,600 per year?


19) A certain aircraft can fly 1330 miles with the wind in 5 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?


20) Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.


21) Khang and Hector live 88 miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector’s rate of speed is 60% of Khang’s. They start out at the same time and meet 5 hours later. Find Hector’s rate of speed.


22) Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $252. The cost of a child’s ticket was $6 less than the cost of an adult’s ticket. Find the price of an adult’s ticket and a child’s ticket.


23) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $8 each and a number of necklaces at $11 each. She wrote a check for $1140 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?


24) Natasha rides her bike (at a constant speed) for 4 hours, helped by a wind of 3 miles per hour. Pedaling at the same rate, the trip back against the wind takes 10 hours. Find find the total round trip distance she traveled.


25) A barge takes 4 hours to move (at a constant rate) downstream for 40 miles, helped by a current of 3 miles per hour. If the barge’s engines are set at the same pace, find the time of its return trip against the current.


26) Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 2 hours on the road. Doreen can maintain a speed of 2 miles per hour, which is 40% of Irena’s speed. If they meet exactly as planned, what is the distance between their houses?



27) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 56% solution and the other an unlimited supply of the 21% solution. How many liters of each solution should Dmitri use?


28) Chandra has 2 liters of a 30% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 6 liters of 46% solution?


29) Jimmy is a partner in an Internet-based coffee supplier. The company

offers gourmet coffee beans for $12 per pound and regular coffee beans for $6 per pound. Jimmy is creating a medium-price product that will

sell for $8 per pound. The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?


30) During the 1998-1999 Little League season, the Tigers played 57 games.

They lost 21 more games than they won. How many games did they win that season?


31) The perimeter of a rectangle is 48 m. If the width were doubled and the length were increased by 24 m, the perimeter would be 112 m. What are the length and width of the rectangle?


32) The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, it would be equilateral. Find the length of the base of the original triangle.


33) The side of an equilateral triangle is 8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the length of a side of the square.


34) The side of an equilateral triangle is 2 inches shorter than the side of a square. The perimeter of the square is 30 inches more than the perimeter of the triangle. Find the length of a side of the triangle.




1) $1.75 for a hot dog; $1.00 for a bag of potato chips 2) 374 senior citizen tickets 3) $3.74 per slice of pizza 4) 12 free throws, 11 field goals 5) 180 miles on the highway, 217 miles in the city 6) 24 rolls of Cloth A, 16 rolls of Cloth B 7) 20 $5 bills 8) 11 nickels and 22 dimes 9) 8 inches

10) length: 26 feet; width: 6 feet 11) first angle = 114°

second angle = 66°

12) 72°, 72°, 36° 13) 3 mm, 9 mm, 9 mm 14) 70 mL of 33%; 60 mL of 85%

15) x = 288 7

, y = 36 7

16) 5 pounds of trail mix 30 pounds of cashews

17) $2000 18) $120,000 at 11% and $40,000 at 6% 19) 38 mph 20) 3 mph 21) 6.6 mph 22) adult’s ticket: $24; child’s ticket: $18 23) 60 bracelets and 60 necklaces 24) 80 mi 25) 10 hr 26) 14 mi 27) 56% solution: 3 L; 21% solution: 4 L 28) 4 L of 54% solution 29) 20 lb 30) 18 games 31) Length: 16 m; width: 8 m 32) 8 cm 33) 22 inches 34) 22 inches


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