Solving Word Problems with Algebraic Formulas
1)  The total age of 5 people is 253.  John is twice the age of Jim, and Frank is 5 years older than Jim.  Wilma is 7 years younger than John, and Linda is 2 years older than Wilma.  How old is each person?  (answer)

2)  A person has 13 coins (quarters and dimes) that totals $2.05.  How many of each coin does he have?  (answer)

3)  If there are 24 coins (quarters, dimes, and nickels) with 4 more the number of dimes than quarters, and it all totals $2.90, how many of each coin is there?  (answer)

4)  Suppose a person has sold two different kinds of inexpensive watches -- one for $20, and the other for $25.   If he made $7,035 by selling 312 of them, how many did he sell of each kind of watch?  (answer)

5)  What five consecutive numbers total 1,285, and with each following number being 5 more than the one before it?  (answer)

6)  Jake, in his car, and Joshua on his bike began their trip at the same time, from the same place, but going in opposite directions.  After three hours, they were 186 miles apart.  If the bike is 26 mph slower than the car, then what were their average speeds? (answer)

7)  It took a small jet 5 hours to make a 1,285 mile trip.  During the last three hours of the flight, it traveled 30 mph slower than it did during the first two hours.  What was its speed for the first two hours?  And what was its speed for the last three hours?  (answer)

8)  Here's a slight variation from our previous example: A small jet made a 1285-mile flight in 5 hours.  Its fastest speed was constant during the first two hours, but then dropped to 30 mph slower during the 3rd hour, 40 mph slower (than the 1st hour) during the 4th hour, and 55 mph slower (than the 1st hour) during the last  hour.  Find the speed for each hour.  (answer)

9)  Mr. Riley runs a corner grocery store.  He sells whole cashews for $4 a pound, and cashew bits and pieces for $3 a pound.  To offer his customers more of a selection, he was planning on mixing up a 100-pound combination of both kinds of cashews to sell for $3.35 a pound.  In order for his profit to remain the same, how many pounds of the $4 cashews, and how many pounds of the $3 bits and pieces would he need to combine for this?   (answer)

10)  After having made 32 ounces of orange-pineapple drink, in which 15% is pineapple juice, Jane decided to increase the pineapple juice to 25%.  To do so, how many ounces of it did she have to pour into the pitcher?  (answer)

11)   On the following day, Jane had made 64 ounces of  her orange-pineapple drink, which is 25% pineapple juice.  After having given 12 ounces of it to her son, who wasn't overly fond of pineapple juice, Jane thought she'd lessen the pineapple juice to just 15%.  To do so, how many ounces of orange juice will she have to add? (answer)

12)  John made some sugarless lemonade (more like lemon-flavored water) that he liked to sip on.  He added 3 ounces of the lemon juice to 32 ounces of water, but quickly realized he added 1 ounce too many of the lemon juice. Fortunately, John knew the right mathematical formulas to help him remedy his problem.  How much water did he have to add to this 35-ounce drink to make the 3 ounces of lemon juice the equivalent (or same percent) as 2 ounces added to 32 ounces would have been?  (answer)
13)  With $15,000, George bought two CDs from two different banks.  One would pay 3% annual interest, while the other would pay 5%.  If his total interest earnings for the year were $650 from these two CDs, then how much had he invested in each one? (answer)

14)  Jill made three investments that yielded $2,260 as annual interest.  Her 7.5% investment was $7,000 more than the one at 5%, and her 8% investment was $1,000 less than six times the 5% investment.   What was the amount she paid for each of these investments? (answer)

15)  Though it takes young Timmy 3 hours to do all the yard work, his father can do the same in 2 hours.  If they both work together, how long will it take? (answer)

16)  If Sam can rake the leaves in the front yard in 35 minutes, and Dave can do the same job in 40 minutes, then how long would it take if they work together?  (answer)

17)  It would take Jake 60 hours to paint his house.  Dennis could do it in 50, and Larry in 53.  If they all work together, how long will it take? (answer)

18)  If it takes Linda 2.5 hours to clean the auditorium, but Hazel can do it in 2, then how long would it take if they worked together?   (answer)

19)  In his shop, Chuck can make a good bookcase in 5 hours.  After working on one for 2 hours, however, he let his son finish it.  The son has made bookcases before, but it takes him 8 hours to make one.  How many hours will it take for the son to complete his father's bookcase?  (answer)

20)  Ben can rake the backyard in 45 minutes.  With his son's help, they can finish the job in 20 minutes.  How long would it take Ben's son to rake all the backyard by himself? (answer)
21)  If 50 pounds were placed on a lever, 3 feet to the left of the fulcrum, how much weight would have to be placed at 5 feet to the right of the fulcrum to have an even balance? (answer)
22)  What distance to the right of a fulcrum would 60 pounds need to be placed for the lever to be balanced, if 75  pounds were 2 feet to the left of the fulcrum? (answer)
23)  If a lever were 12 feet long, with 75 pounds on one end and 45 pounds on the other, where would the fulcrum have to be placed to balance it? (answer)
24)  Where would you place the fulcrum for a 33-foot lever, if at one end there is 100 pounds and 60 pounds on the other? (answer)

25)  If a 40-foot pole will cast a shadow that is 75 feet long, then how long would the shadow be (at the same time) of a 6-foot man who is standing beside that tree? (answer)
26)  If 12 gallons of gas cost $16.68, then how much would 17 gallons of gas cost? (answer)

27)  If 8 quarts of oil cost  $10.64, how much would 6 quarts cost?  (answer)
28) In the will, $375,000 was to go toward the deceased woman's only son and her only grandchild.  Since the ratio between the son's and the grandson's inheritance was 8:2, how much did each receive (with the son receiving the lion's share)?   (answer)
Using Two Variables

29)  Andy and Lonnie were trying to remember how much the cokes and pizza slices were at the corner restaurant.   Recently, they had bought 2 cokes and 5  pizza slices for 16.85; and a couple days earlier, they bought 4 cokes and 3 pizza slices for $13.05.   What is the cost of each pizza slice and each coke?    (answer)
30)  If 3 cans of mushrooms and 5 cans of 3-bean salad cost $5.90, and 2 cans of mushrooms and 4 cans of 3-bean salad cost $4.52, then how much is each can of mushooms, and each can of 3-bean salad?    (answer)
31)  Traveling from Dallas to Atlanta, a jet was able to average 760 mph, due to a tailwind.  On the return flight, however, it averaged just 682 mph against the wind.  What was the speed of the wind, and what would the speed of the jet have been without it?    (answer)
32) Roxanne had 39 coins (quarters and dimes) that totaled $7.80.  How many of each coin did she have?    (answer)

33)  With $35,000, Bill made two investments.  Since one paid 8% interest, and the other 12%, his total intererest-earning for these two was $3,920 for the year.  How much had he initially invested at each percent?    (answer)