Mathematical Word Problems

Mathematical Word Problems

Tutorial


• The key to word problems is to read the question thoroughly and slowly. Don’t be overwhelmed. Just break it down and write it out step by step. If necessary, draw diagrams to help you understand the scenario.


• Take each sentence individually and investigate the information it gives you. Think of yourself as a Crime Scene Investigator (CSI), solve the mystery, and watch the answer unfold before your eyes….


• Number One• Problem: Brienne owns four cars.

Gavan owns twice as many cars as Brienne. Ashley owns one less car than Gavan. Ashley is buying four new tires for every car she owns. Each tire costs one hundred dollars. How much money will the tires cost altogether?


• Solution: We need to break this down and dissect the information in each sentence.

• First… Brienne owns four cars… So Brienne owns 4 cars.

• Second… Gavan owns twice as many cars as Brienne…. So…2 x 4 = 8 cars for Gavan.

• Next…. Ashley owns one less car than Gavan…. So…8 – 1 = 7 cars for Ashley.

• Now…. Ashley is buying four new tires for every car she owns… So… 4 x 7 = 28 tires

• Last…Each tire costs one hundred dollars….So… $100 x 28 = $2800 for her new tires.


• Number Two• Problem: Anthony and Carolyn have bug

collections. If they combined their collections, they would have a collection of twenty bugs. Which of the following statements could not be true?

• a. Carolyn has a dozen bugs.b. Anthony has eleven bugs.c. Anthony has one more bug than Carolyn.d. Carolyn has two more bugs than Anthony.e. Carolyn has one bug.


• Solution: Again, each sentence in the multiple choice needs to be dissected to find the one that is false. The key is that the total bugs are 20.

• Can Carolyn have a dozen bugs? If she has 12, then Anthony has 8 because 20-12=8

• This could be true.• Can Anthony have eleven bugs? If he

has 11, then Carolyn has 9 because 20-11=9

• This could be true also.


• Can Anthony have one more bug than Carolyn? This one takes some thought. But if you use the two examples above, you can easily decipher this one. If Anthony has 11 bugs for instance, can Carolyn have 10? No because that would = 21 bugs between them. Well, can Anthony have 10 and Carolyn have 9 bugs? No because that would =19 bugs between them. Notice that one cannot have an even number and the other an odd number of bugs. The total 20 is an even number. This indicates that both will have even numbers of bugs or both will have odd numbers of bugs. (Note the first two possible answers.)


• This is obviously your FALSE statement, but with all word problems it is wise to read the rest of the options just in case there it more than one answer. This also solidifies your confidence in your answer or can help you recognize a mistake in your calculations.

• Can Carolyn have two more bugs than Anthony? True. This is demonstrated above in the second possible answer where Anthony has 11 and Carolyn has 9.

• Can Carolyn have one bug? True. Anthony could easily have 19 of the bugs.


• Number Three

• Problem: There were 24 apples given out to the children at Faith’s Halloween party. Each child got three apples. How many children were at the party?


• Solution: Once again, pay attention to all the information given.

• We have 24 apples.• Each child got 3 apples.• There are more apples than children if

each got 3 apples.• So we divide 24 apples by 3 apples and

we get 8 children.• 24 / 3 = 8 or another way to look at it is:

? x 3 = 24 The answer is still 8.


• Number Four

• Problem: How many ghosts are in the haunted house? Here are some clues: There are more than the number of days in October. There are less than the product of 7 and 5. The answer is an odd number.


• Solution: October has 31 days, so the number is > 31.

• We are also told that the number is less than the product of 7 and 5.

• Hint: Product = multiplication

• Sum = addition

• Difference = subtraction


• Ratio = division• However, even not knowing the word

product means multiply, we know that if we add 7+5 we get 12 and the number can’t be less than 12 and greater than 31 at the same time. But if we multiply, we get 7 x 5 = 35. So the number is < 35.

• Now the answer comes easily….which number is > 31 and < 35 and an odd #?

• 31, 32, 33, 34, 35


• Number Five• Problem: Sandra is playing in a

tennis doubles tournament. The rules say that the average age of the pair of players on each side must be ten years old or younger. Sandra is eight years old. Her partner must be _____ years old or younger.


• Solution: Here the average age must be 10 years old.

• This means that if there are 2 players and if we add their ages together and divide by 2 it has to be at least 10!

• So the least their combined age could be would be 20 because… 20 / 2 = 10

• If their combined ages totaled 24, then 24 / 2 = 12 and they still meet the minimum age requirements.

• However if their combined age was 18, then 18 / 2 = 9 and this is less than the minimum age requirement.


• So Sandra and her partner together must = 20. If Sandra is 8, then her partner must be 20 – 8 = 12 years old.

• Does this work? Let’s check our work:• 8 yrs old + 12 yrs old = 20 years old….

Divide by 2 for the average age of 10!• Good luck in the tournament girls….• And now good luck to you as you take

the exam for this module!


You must make a perfect score of 100% to pass.

Click here to take the test for this module.

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Mathematical Word Problems