Strategies to Simplify Word Problems Practice Questions

To review these concepts, go to Strategies to Simplify Word Problems Study Guide.

Strategies to Simplify Word Problems Practice Questions

Practice 1

Try the problems in the following practice set to apply the strategy of solving a simpler problem.

Problems

Charlotte has $62 to spend on new clothes. She would like to buy a shirt for $14.99, a pair of pants for $19.99, and a new pair of shoes for $24.99. If there is no sales tax on the items, does she have enough money to buy all three?
What is the sum of the first 10 even natural numbers?

Solutions

Read and understand the question. This question asks if there is enough money to buy three items. The total amount of money Charlotte has to spend and the price of each item is given.

Make a plan. Make the problem simpler by adjusting the values. Use rounding to make the numbers easier to use.

Carry out the plan. Round the price of the shirt from $14.99 to $15.00, round the price of the pants from $19.99 to $20.00, and round the price of the shoes from $24.99 to $25.00. Add the rounded amounts of each item: $15 + $20 + $25 = $60. She has enough money to pay for the items.

Check your work. When adding the rounded amounts, she has $62 – $60 = $2 left over. Because each of the prices was rounded up, she would actually have slightly more than $2.00 left over.

Read and understand the question. This question is looking for the sum of the first 10 even numbers. The even numbers are 2, 4, 6, 8 …

Make a plan. This problem seems difficult when you are trying to add all 10 values. Begin by making the problem simpler by adding just a few numbers, and then look for a pattern.

Carry out the plan. You need to add the first 10 even numbers. This would appear as 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20. However, instead of adding the numbers in order, begin by adding the first and the second-tolast number: 2 + 18 = 20. Continue this pattern using the next numbers: 4 + 16 = 20, 6 + 14 = 20, 8 + 12 = 20. The values of 10 and 20 in the list will not have a paired value. Therefore, there are four sums of 20, plus the number 10 and the number 20: 4 × 20 + 10 + 20 = 80 + 10 + 20 = 110. The sum is 110.

Check your work. One way to check your work is to add the numbers in the list by hand or with a calculator. Each of these methods results in a sum of 110.

Practice 2

The following question set provides practice on using the strategy of guess and check. Try these problems and make use of this approach to make the problems easier to solve.

Problems

A person spots a number of birds and squirrels in a park. Each squirrel has 4 feet, each bird has two feet, and there are a total of 24 feet among all of the animals. If there are 3 more squirrels than birds, how many of each animal is in the park?
Hannah is half as old as her aunt. The sum of their ages is 42. How old is Hannah?
Henry ate two less than triple the number of candies that Noah ate. If they ate a total of 30 candies, how many did each person eat?

Solutions

Read and understand the question. In this question, you are seeking the number of birds and the number of squirrels spotted in a park. The fact that there are 3 more squirrels than birds is given. It is also given that there are 24 feet between the animals.

Make a plan. Use the strategy of guess and check to solve this problem. Show at least three guesses for the number of birds and number of squirrels, and be sure that the number of squirrels is 3 more than the number of birds.

Carry out the plan. Begin with the guess of 4 squirrels and 1 bird. This would be a total of 4 × 4 = 16 feet for the squirrels and 2 × 1 = 2 feet for the bird. This is a total of 18 feet. This guess is too low.

For the next guess, try 6 squirrels and 3 birds. This would be a total of 6 × 4 = 24 feet for the squirrels and 3 × 2 = 6 feet for the birds. This is a total of 30 feet, which is too high.

Now, try a guess of 5 squirrels and 2 birds. This would be a total of 5 × 4 = 20 feet for the squirrels and 2 × 2 = 4 feet for the birds. This is a total of 24 feet, which is the correct answer.

Check your work. Check your answer to be sure that it fits all of the information in the question. There are a total of 24 feet among the animals, and there are 3 more squirrels than birds. Five squirrels is 3 more than 2 birds, and there are a total of 20 + 4 = 24 feet among them. This answer is checking.

Read and understand the question. This question is looking for Hannah's age. She is half as old as her aunt. If you add their ages, the sum is 42.

Make a plan. Apply the strategy of guess and check to solve this problem. Try a number for Hannah's age and then double it to represent her aunt's age. See if the sum of the two ages is equal to 42.

Carry out the plan. The sum of their ages is 42, and half of 42 is 21. Since you are going to be adding a number and double that same number, begin your guesses with a value somewhat smaller than 21. Try a guess of 12 for Hannah's age. Her aunt's age would then be 12 × 2 = 24. The sum of these ages is 12 + 24 = 36. This is too low.

Try the next guess of 16 for Hannah's age. Her aunt's age would then be 16 × 2 = 32. The sum of these ages is 16 + 32 = 48. This is too high.

For the next guess, use 14 for Hannah's age. Her aunt's age would then be 14 × 2 = 28. The sum of these ages is 14 + 28 = 42. This is the correct answer.

Check your work. Check to make sure that the answer fits all of the information given in the question. Since Hannah is half as old as her aunt, 14 is half of 28. The sum of their ages is 42, so check the sum of their ages: 14 + 28 = 42. This answer is checking.

Read and understand the question. You are looking for the number of candies each person ate. The total number of candies is given, along with the fact that Henry ate two less than triple the number that Noah ate.

Make a plan. Use the strategy of guess and check. Start with an amount for Noah, then triple this amount and subtract 2. Make sure that the amounts for each person add to 30.

Carry out the plan. There are a total of 30 candies, so half of this amount is 15. Start the first guess below this amount.

Try 10 candies for Noah. Then, Henry ate 10 × 3– 2 = 30 – 2 = 28 candies.

This is a total of 10 + 28 = 38 candies. This guess is too high.

Try 5 candies for Noah. Then, Henry ate 5 × 3 – 2 = 15 – 2 = 13 candies.

This is a total of 5 + 13 = 18 candies. This guess is too low.

Try 7 candies for Noah. Then, Henry ate 7 × 3 – 2 = 21 – 2 = 19 candies.

This is a total of 7 + 19 = 26 candies. This guess is too low, but very close to the correct answer. Remember, do at least three trials for each problem, but it may take more to find the solution.

Try 8 candies for Noah. Then, Henry ate 8 × 3 – 2 = 24 – 2 = 22 candies.

This is a total of 8 + 22 = 30 candies. This is the correct answer.

Check your work. Check your work by making sure that your answer fits the information given in the question. Henry ate two less than triple the amount that Noah ate. Since Noah ate 8 candies, two less than triple this amount is 24 – 2 = 22 candies. The total number of candies was 30, and 22 + 8 = 30. This answer is checking.

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Strategies to Simplify Word Problems Practice Questions