Education.com
Try
Brainzy
Try
Plus

# The Strategies of Working Backward and Using Logical Reasoning in Word Problems Practice Questions

(not rated)
By
Updated on Oct 3, 2011

To review these concepts, go to The Strategies of Working Backward and Using Logical Reasoning in Word Problems Study Guide.

## The Strategies of Working Backward and Using Logical Reasoning in Word Problems Practice Questions

### Practice 1

The questions in the practice set that follows can be simplified by using the strategy of working backward. Try this strategy for each, and then use the answer explanations at the end of the section help refine this method of finding a solution.

#### Problems

1. A child is playing with blocks. There are twice as many green blocks as red blocks. The number of blue blocks is five more than the number of red blocks. If there are 15 blue blocks, how many blocks of each color are there?
2. Sheila attended the local fair. She spent \$5.50 playing games and spent double that amount on rides. She then spent \$2.25 on an ice cream cone. If she had \$4.25 left over, how much money did she bring to the fair?
3. On the first day of harvesting vegetables, a farmer picked three-fourths of his ears of corn. On the second day, he harvested half of the ears that were left. On the third day he harvested the remaining 50 ears. How many total ears of corn did he harvest?

#### Solutions

1. Read and understand the question. The question is asking for the number of blocks of each color when clues are given about the number of each.

Make a plan. Use the strategy of working backward to solve this problem. Start with the fact that there are 15 blue blocks and use the inverse (opposite) operations when necessary.

Carry out the plan. Because there are 15 blue blocks, and the number of blue blocks is 5 more than the number of red blocks, there are 15 – 5 = 10 red blocks. There are twice as many green blocks as red blocks. Therefore, there are 10 × 2 = 20 green blocks. There are 15 blue blocks, 10 red blocks, and 20 green blocks.

Check your work. Work forward through the question to check your work. Start with 20 green blocks. This is twice as many as the number of red blocks, so the number of red blocks is 10. The number of blue blocks is 5 more than the number of red blocks, so 10 + 5 = 15 blue blocks. Since this was given in the question, this solution is checking.

2. Read and understand the question. The question is asking for the total amount of money Ella had before she went to the fair.
3. Make a plan. Start with the amount of money left over, and use the strategy of working backward to find out how much she had at the start of the fair.

Carry out the plan. Begin with the \$4.25 left over. Since she spent \$2.25 on an ice cream cone, add \$4.25 + \$2.25 = \$6.50. She also spent \$5.50 on games, so add \$6.50 + \$5.50 = \$12.00. She spent twice as much on rides as she did on games, so she spent \$5.50 × 2 = \$11.00 on rides. Now, add \$12.00 + \$11.00 = \$23.00, which is the total amount of money she brought to the fair.

Check your work. Work forward through the question to check your work. She started with \$23.00 and then spent \$5.50 on games. \$23.00 – \$5.50 = \$17.50. She spent twice as much on rides as on games, so subtract: \$17.50 – \$11.00 = \$6.50. She then bought an ice cream cone for \$2.25: \$6.50 – \$2.25 = \$4.25. Since this is the amount of money she had left over, this answer is reasonable.

4. Read and understand the question. The question is looking for the total number of ears of corn harvested after he worked for three days.
5. Make a plan. Start with the fact that the farmer harvested 50 ears the third day, and use the strategy of working backward to the first day.

Carry out the plan. Start with 50 ears the third day. On the second day, he harvested half of the ears that were left, and 50 ears remained. This means that there were 100 ears on the second day and he harvested 50 of them. On the first day, he harvested three-fourths of the total number of ears. Since there were 100 ears on the second day, this represents one-fourth of the number of ears. If 100 is equal to one-fourth, then 300 is equal to threefourths: 100 + 300 = 400 total ears were harvested.

Check your work. Start with the solution and work forward through the question to check your work. He began with 400 ears in the field. The first day he harvested three-fourths, so 300 of the 400 ears: 400 – 300 = 100 ears remain. The second day, he harvested half of what was left, so 50 ears: 100 – 50 ears remain. The final day he harvested the remaining 50 ears. This answer is checking.

150 Characters allowed