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Fraction Problems--Selling and Purchasing: Math in the Real-World of 2009 |
Daniel
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A salesperson named, Chris, travels to city selling laptops. Each full mile he travels, he sells 7 laptops. From the first city to the second city is 3 4/5 miles. The second city to the third city is 5 7/10 miles. The third city to the fourth city is 14 2/3 miles. After Chris finished in the fourth city, he went back to the first city but did not stop to sell laptops. There were only 4 laptops left.
How many miles did he travel?
How many laptops did Chris sell?
How many laptops did Chris have in the first place? |
Ben |
Mr. Ray has two cookie cakes to sell. On Sunday, Mrs. Beach came in and bought ½ of the first cake. On Monday, Mr. Perez bought 2/8 of the first cake. Then, Joe bought 3/16 of the first cake. Then, Raymond bought 2/32 of it. On Tuesday, Juan bought 4/8 of the second one. Then, Mr. Lopez bought 10/32 of the second one. How much of the two cookie cakes will be left now? |
Christopher
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Bob is making a wooden stool. Bob knows the length of all of the pieces but has to find the total amount of wood that is needed to make 1 stool. He knows that there are 4 legs and each leg is 1 ¼ feet tall and 2 inches wide. He also knows that to make the seat there has to be 4 pieces of wood and each piece is 1/6 of a foot longer than each leg. If each plank comes in 6 feet lengths and the plank’s width is cut correctly at the store, how many planks of wood will he need? How many feet and inches of wood will Bob need to make 1 stool? How many feet and inches will he need to make 4 stools? |
Andrew
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Joe is delivering cookies in Cookieville. He has one mile to go before he meets his next customer, but every five feet he hits a bump in the road. Every time he hits a bump one of his 2500 cookies breaks in half.
A. How many bumps are there?
B. How many whole cookies does Joe have when the mile is driven?The customer wants 1500 whole cookies.
C. The customer wants 1500 whole cookies. Can Joe fill this order? |
Alex
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A man is selling quarts of ice cream to customers in the Whole Foods store. The flavors are vanilla, chocolate chip, strawberry and Superman. A. Sam came in and bought 3 3/8 gallons of ice cream. Howard came in and bought 4 5/8 of gallons of ice cream. How many quarts did both customers buy?
B.1/4 of all the ice cream bought was Chocolate Chip. 1/8 of all the ice cream the men bought was strawberry. The rest was Superman. How many quarts were Superman? |
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Solutions |
| Daniel |
Question 1: You have to add all the miles Chris traveled from one city to another. The number model would be 3 4/5 + 5 7/10 + 14 2/3=? You would want to make all the denominators the same, so thirty would be it because thirty is a multiple of 5,10, and 3, so the new denominators is 30. Now you have to find the new numerators. After you find the numerators, your new number would be 3 24/30 + 5 21/30 + 14 20/30= 24 5/30= 24 1/6 miles. It said that Chris went back to the first city when he was done at the fourth city. So you’ll have to double the amount to show the return trip. Your final answer would be 24 5/30+ 24 5/30= 48 18/20= 48 1/3 mile trip.
Question 2: The question asks how many laptops he SOLD. You know that each mile he travels, he sells 7 laptops and that Chris took a 24 and about a half mile trip selling laptops. You would drop the fraction because he needs a full mile to sell 7 laptops. You would multiply 24*7 because each full mile he sells 7 laptops and that he didn’t sell laptops on the return trip. Your final answer would be 168 laptops sold.
Question 3: You would use the answer from question number 2 to help. It also said that he had 4 laptops left. You add 4 + 168 = 172 because it asks how many he had in all. You answer would be that he had 172 laptops in the first place. |
| Ben |
Explanation: First, I added 1/2 + 2/8+3/16+2/32 of the first cake. I converted ½ into 4/8 which I the converted into 16/32. Then I converted 2/8 into 8/32. Then I converted 3/16 into 6/32 and then added everything together to get 32/32, which is 1. So, one cookie cake is gone. Then, for the second cake I have to add 10/32+ 4/8. I converted 4/8 into 16/32, because 8 goes into 32 four times. So, 16/32+10/32=26/32. I subtracted 26/32 from 32/32 and got 6/32. Then, I converted 6/32 into 3/16 and that was my answer. |
| Christopher |
First I found out that 1 ¼ feet is equal to 15 inches because 1 foot is 12 inches and ¼ feet is 3 inches. I added 12 in. + 3 in. and got 15 inches. Then I multiplied 15in. *4 and got 60 inches or 5 feet. I did that because there are 4 legs and each leg is 15 inches. Then I found out that 1/6 of a foot is equal to 2 inches. Next I added 2 inches + 15 inches because each seat piece is 2 inches longer than the 15 inch legs. The sum is 17 inches. I multiplied 17 inches * 4 because there are 4 seat pieces and each seat piece is 17 inches long. Bob will need 68 inches or 5 feet and 8 inches of wood to build one stool. To find out how many inches of wood are needed to make 4 stools I multiplied 68 inches * 4 because one stool is 68 inches and there are 4 stools. Bob will need 272 inches or 22 feet and 8 inches of wood to make 4 stools. Bob will need 4 planks of wood to make 4 stools. |
Andrew
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A. 1856
B. 644
C. No
First I needed to find out how many bumps Joe would hit so I divided 5820 by 5. Five was my divisor because of the bump every 5 feet. 5280 was my dividend because there are 5280 feet in a mile. I got 1856 as my quotient. That answered my first question. Then I needed to know how many whole cookies he had when the mile was over. So I subtracted 1856 from 2500 to get 644. That answered my second question. The customer wanted 1500 whole cookies. Joe had 644 whole cookies so he could not fill this order. That answered the third question. |
Alex |
A. First I added my fractions. My problem was 3 3/8 + 4 5/8 = 7 8/8 = 8. To find out how many quarts are in the gallons, multiply by four. My answer is 32 quarts.
B. First I divided 32 by 4 to get the answer for the ¼ of the quarts of ice cream. I got an answer of 8. Then I divided 32 by 8 to get the answer for the 1/8 of all the ice cream. I got an answer of 4. Then I added them up (4 quarts + 8 quarts = 12 quarts) and subtracted the answer from 32 quarts to get an answer of 20 quarts of Superman ice cream. |
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Speedy Problems |
Brian
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One day, all the turtles from a nearby pond, all the chipmunks from a nearby plain, all the rabbits from the nearby burrows, and all the sparrows from a nearby nest decided to race.
When they reached the starting point of the 11th story of the John Hancock Building in Chicago, which is 1,127 feet tall and 100 stories tall. They started the race.
“Go!!!” yelled the starter. They embarked on their journey to the train station in Arlington Heights, IL. They all traveled at different speeds. The sparrows started to travel at a speed of 15mph. The rabbits, close behind, traveled at 14mph. Speeding in 3rd place, the chipmunks were running as fast as their little feet could carry them, 12mph. Trotting slowly, but at a steady pace, the turtles were going 10 mph. After two hours of the journey, both the rabbits and the sparrows got tired and slowed down to a mere 11mph. Also, at around two hours, the chipmunks left a note for the turtles taunting them to move faster. Four miles later, the turtles found the note and got vvvveeeeeeeeerrrrrrryyyyyyyy angry. With a full head of steam, they ran 16 mph. After the chipmunks figured out that the turtles might get mad and try to catch them, they ran 14mph.If they all kept moving at their pace for 2.5 more hours, who will win the race? Who will come in 2nd, 3rd, and last place?
Challenge:
If the chipmunks slow back down to 8mph, and the sparrows speed up to 13mph and they all decide to run for one more hour, in addition to the 4 1/2 previous hours, what would the rankings be?
Double Challenge:
Multiply the leaders miles ran (in the original) by 79 then divide it by 4 and add 123 what will the answer be?
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Konrad |
Speedy Problem
By Konrad
One blazing hot day in Chicago, Illinois, a car, my brother, an airplane, and a snail lined up by the Sears Tower to start their voyage to Orlando, Florida which is 1,115 miles away from the Windy City.
My brother started the trip at a pace of 7 MPH until he reached the halfway point, then he slowed down to 3 MPH. The car sped at 135 MPH for the whole trip. The airplane on a truck on the highway traveled at 50 MPH and the snail snailed at a whopping pace of 6 MPH. If all the travelers left Chicago watching the skyline fade away and reached their destination in Orlando, Florida what would be the sum of their times rounded to the nearest hour?
* Round all numbers used when solving the problem to the ones place
Challenge
What would be the time of the airplane if it fell off the truck because of a tire blow out 795 miles into the trip and it skidded 20 MPH till its original location?
Bonus Challenge
Multiply the answer to the last question by 56 :) |
Brian
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Part One: Solution
First, I made the following chart:
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Different Times |
Rabbits |
Turtles |
Chipmunks |
Sparrows |
A |
First Two Hours |
28 Mph |
20 Mph |
24 Mph |
30 Mph |
B |
Next Two And ½ Hours |
27.5 Mph |
40 Mph |
34 Mph |
27.5 Mph |
C |
Total |
55.5 Mph |
60 Mph |
58 Mph |
57.5 Mph |
To find the answer to part A, I multiplied their beginning speed by two. Then I filled in row A.
For part B I did 3 things: 1) I divided their changed speed by two, 2) I multiplied that same changed speed by two. 3) Then I added both of those together to get row B.
Lastly, I added row A and B to get row C.
1st turtles
2nd chipmunks
3rd Sparrows
4th rabbits
Part Two: Challenge
To find the answer you make a chart like the one above, but add a row.
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Different Times |
Rabbits |
Turtles |
Chipmunks |
Sparrows |
A |
First Two Hours |
28 Mph |
20 Mph |
24 Mph |
30 Mph |
B |
Next Two And ½ Hours |
27.5 Mph |
40 Mph |
34 Mph |
27.5 Mph |
C |
Final hour |
11 Mph |
16 Mph |
8 Mph |
13 Mph |
D |
Total miles ran |
66.5 Mph |
76 Mph |
66 Mph |
70.5 Mph |
Then you add all the numbers in rows A, B, C, in your select columns.
1st 76 mph the turtles ran
2nd 70.5 mph the Sparrows flew
3rd 66.5 mph the rabbits sprinted
4th 66 mph the Chipmunks scurried
Part three: Double Challenge
First you multiply 60 by 79 to get 4740 than divide 4740 by four to equals 1185 than add 123 to equal your answer 1308 turtles.
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Konrad |
Speedy Problem
By Konrad
SOLUTION
First I figured out what is half of 1115 miles, the total length of the trip. Then I divided my answer, 557.5 miles, by 7 MPH, the speed my brother ran at half the race. I got the answer of 80 hr. Then I divided 557.5 by 3 MPH, the other speed he ran at. I received the answer of 186 hr. I got the total of 266 hr.
Next I divided 1115 miles, the length of the trip, by 135 MPH, speed of the car. I discovered the answer 8 hr Then I separated 1115 miles by 50 MPH, the speed of the airplane on the truck. I got the answer of 22 hr.
On the fourth step I divided 1115 miles by the whopping speed of the snail, 6 MPH. I got the answer of 186 hr.
Lastly I added all the answers, 266 hr., 8hr., 22hr., and 186 hr witch equals 482 hr.
Challenge
First I figured out how long it took the plane to travel 795 miles, distance traveled with out problems, and divided it by the speed it was traveling, 50 MPH. I got 16 hr of travel time before the tire blow out.
Then I found out that 320 miles, the length the plane skid, divided by 20 MPH, speed traveled during skid, is 16 hr.
Lastly I added 16 hr. and 16 hr. to get the total of 32 hr.
Bonus In Challenge
I used traditional multiplication to answer 56x32 hr. I got the answer of 1,792 hr. |
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