# Systems of Equations

Systems of Equations
1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot 1) 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 2) 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 3) 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 4) 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?
Julio has found that his new car gets 36 miles per gallon on the highway 5) 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 6) 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 7) bills is \$780. How many \$5 bills are there?
Jamil always throws loose change into a pencil holder on his desk and 8) 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?
A flat rectangular piece of aluminum has a perimeter of 60 inches. The 9) length is 14 inches longer than the width. Find the width.
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Jarod is having a problem with rabbits getting into his vegetable garden, 10) 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 11) 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 12) 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 13) 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 14) 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 15) 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 16) 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?
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17) Kelly is a partner in an Internet-based seed and garden supply business. 17) The company offers a blend of exotic wildflower seeds for \$95 per
pound and a blend of common wildflower seeds for \$30 per pound.
Kelly is creating a medium-price product by mixing together 33 pounds
of the more expensive blend with 6 pounds of the less expensive blend. What will be the price per pound for the new blend? (Round to the nearest cent, if necessary.)
18) A college student earned \$7300 during summer vacation working as a 18) 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%?
. 19) A retired couple has \$160,000 to invest to obtain annual income. They 19) 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?
20) A certain aircraft can fly 1330 miles with the wind in 5 hours and travel 20) the same distance against the wind in 7 hours. What is the speed of the
wind?
Julie and Eric row their boat (at a constant speed) 40 miles downstream 21) 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.
. 22) Khang and Hector live 88 miles apart in southeastern Missouri. They 22) 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.
. 23) Devon purchased tickets to an air show for 9 adults and 2 children. The 23) 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.
. 24) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of 24) 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?
. 25) Natasha rides her bike (at a constant speed) for 4 hours, helped by a 25) 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.
3
. 26) A barge takes 4 hours to move (at a constant rate) downstream for 40 26) 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.
27) Doreen and Irena plan to leave their houses at the same time, roller 27) 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?
28) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research 28) 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?
29) Chandra has 2 liters of a 30% solution of sodium hydroxide in a 29) 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?
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?
. 31) During the 1998-1999 Little League season, the Tigers played 57 games. 31) They lost 21 more games than they won. How many games did they win
that season?
32) The perimeter of a rectangle is 48 m. If the width were doubled and the 32) length were increased by 24 m, the perimeter would be 112 m. What are
the length and width of the rectangle?
33) The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if 33) 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.
34) The side of an equilateral triangle is 8 inches shorter than the side of a 34) 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.
4
The side of an equilateral triangle is 2 inches shorter than the side of a 35) 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.
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