Algebra

The sum of two numbers is 19. Their difference is 5. Find the numbers. (7 and 12)
2) One number is 8 more than three times another. If the sum of the numbers is 16, find the
numbers. (2 and 14)
3) One number is 4 less than 3 times another number. If the sum of the numbers is 36, what
are the numbers? (10 and 26)
4) The length of a rectangle is 18 inches more than two thirds of its width. If the perimeter of
this rectangle is 96 inches, find its dimensions. (Length = 30 inches, Width = 18 inches)
5) The perimeter of a rectangle is 102. The width is 3 more than one fifth its length. What is
the width of the rectangle? (Width = 11 feet)
6) Fernando bought five shirts and four pairs of socks for $87. He returned to the same store a
week later and purchased, at the same prices, two shirts and six pairs of socks for $48. How
much is each shirt and each pair of socks? (Shirts are $15 each and Socks are $3)
7) Jen Vasquez has been pricing Speed-Pass train fares for a group trip to New York. Three
adults and four children must pay $89. Two adults and three children must pay $63. Find
the price of an adults ticket and the price of a childs ticket. (Adult $15, Child $11)
updated 11/13/2018
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8) A collection of 20 coins consisting of dimes and quarters has a total value of $3.95. How
many of each type of coin are there? (13 quarters and 7 dimes)
9) Susan has $1.45 in nickels and dimes. She has 4 more dimes than nickels. How many
nickels and how many dimes does she have? (7 nickels and 11 dimes)
10) The owner of a candy store wishes to mix candy selling for $1.50 per pound with nuts
selling for $1.00 per pound to obtain a party mix to be sold for $1.20 per pound. How many
pounds of each must be used to obtain 50 pounds of the mixture? (20 lbs of candy and 30 lbs of nuts)
11) How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 pounds
of corn that cost $0.50 per pound to make a mixture of vegetables that costs $0.65 per
pound? (9.6 pounds of lima beans)
12) Susan wants to make 16 liters of a 35% alcohol solution by mixing together a 90% alcohol
solution and a 10% alcohol solution. How much of each solution must she use? (5 liters of 90%
solution and 11 liters of 10% solution)
13) If the width of a rectangle is 9 feet less than twice its length, and the perimeter is 30 feet,
what are the dimensions of the rectangle? (Length = 8 ft, Width = 7 ft)
14) Carol invests $2500 for one year. She invests part in a bond paying 5% and the rest in a
fund paying 3%. If the total interest received is $95.00, how much did Carol invest in each?
($1000 in the bond and $1500 in the fund
15) Three friends have test scores that are consecutive integers. The sum of their test scores is
246. What are the scores? (81, 82, 83)
16) The sum of three consecutive even integers is 174. What are the integers? (56, 58, 60)
17) Four odd consecutive integers have a sum of 96. What are the integers? (21, 23, 25, 27)
18) A plane traveled to Beijing and back. The trip there was with the wind and took 4 hours.
The trip back was into the wind and took 8 hours. If the distance is 432 miles each way,
what is the speed of the plane in still air? What is the speed of the wind? (Airplane in still air is 81
mph, Wind is 27 mph.)
19) Michelle and Chris leave by car from the same location traveling in opposite directions.
Michelle leaves at 2pm driving at 55 mph, while Chris leaves at 3pm driving at 45 mph. At
what time will they be 280 miles apart? (At 5:15 pm, 3.25 hours after Michelle leaves)
20) While training for an iron man competition, Tony bikes for 42 miles and runs for 29 miles.
If his biking speed is 6 times his running speed, and it takes him 6 hours to complete the
training, how fast does he bike? (Tony bikes at 36 mph.)
21) One number is six more than another. If their ratio is 7 to 9, what are the numbers? (21 and 27)
22) In a boutique, a $145 scarf is marked “25% off.” How much is the discount and what is the
sale price of the scarf? (Discount $36.25, sale price $108.75

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