Cylinder, again

The diameter of the base of a cylinder barrel is 20 inches. If it is 25 inches deep, what is the volume of the cylinder barrel?

how much is the jacket?

A jacked is \$105.00. If the price is reduced by 2/7 , how much will it be?

Please find the answer and the worksheet for another similar problems here

how much does the jacket cost?

A pair of pants cost \$75.00 and it costs 2/3 as much as a jacket. How much does the jacket cost?

Matthew weighs 48 pounds. If he 3 /8 as much as his dad, how much does his dad weigh?

The purpose of these problems is to prepare students with standardized testing. To be able to find the amount in 1 is the key to solve all the fraction word problems.

To find the answers and a total of 10 word problems of this type, please visit here

Share a watermelon

Mom bought one big watermelon for the hot day. My brother was so thirsty that he wanted half of the watermelon. Mom cut the watermelon into two sections and gave my brother the larger section. Then she asked: ”Is this half of the watermelon that you wanted?” My brother said: “yes, yes. ”

“No. When a watermelon is cut into halves, your section and your brother’s should be the same big.”

“Oh! Half a watermelon means that the two sections of the watermelon are the same. Brother, next time, I will make sure that mom cuts the watermelon into two same sections so that you and I each can have a section of the same big.”

cutting a stick

Can you solve this problem?

1/8 of a stick is cut off. If If another stick that is 15 inches long is glued to the remaining part of the first stick, the first stick will be 1/2 longer than its original length. What is the original length of the first stick?

In this problem, you need to find the match between the fractional part and the amount in it ( if you do not know about these terms, please go to Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12)

15 inches  not only has covered  1/8 of the stick that is cut off but also makes the  the stick 1/2 longer so we can say that 15 inches match the sum of the fractional parts: 1/8 and 1/2.

We divide the sum of the fractional parts: 1/8+1/2=5/8 into the amount that matches it: 15 inches to find the amount in 1, which is the length of the original stick: ( please go to the books Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12 for more detailed explanation):

15÷5/8=24 inches

The original stick is 24 inches.

Keys and locks

There are 6 keys and 6 locks. At most how many tries are required before it is certain that each lock has found its key?

One answer is as follows: 6 x 6=36 tries ( Is this correct?)

The other answer is as this:

1. Use the 6 keys to try 1 lock at a time and at most 5 tries are required before the lock finds its key. Move the key and lock away from the groups. Now there are 5 locks and 5 keys left.
2. Use the 5 keys to try another lock and at most 4 tries are required before the lock finds its key. Move the second set of key and lock out of the groups. Now there are 4 locks and 4 keys left.
3. Use 4 keys to try another lock and at most 3 tries are required before the lock finds its key. Move the third set of key and lock out of the groups. Now there are only 3 locks and 3 keys left.
4. Use the 3 keys to try another lock and at most 2 tries are required before the lock finds its key. Now more the fourth set of key and lock out of the groups. Now there are only 2 locks and 2 keys left.
5. Use the 2 keys to try one of the remaining locks and at most 1 try is required for the lock to find its key.  Move the 5th set of key and lock out of the groups. Now there are only 1 key and one lock left and they should be one set.

How many tries are there from the above steps?

5+4+3+2+1=15 tries

Of course, the second answer is correct. When you see a verbal problem, do not rush to get  the answer. Always think it through.

job efficiency

John’s neighbor, Mrs. Lee, will pay John \$360.00 when John finishes planting the flowers in her garden  within certain number of days. John has worked for 6 days but has only planted 1/3 of all the flowers. He knows that if he does not finish the job on time, he will not get paid the full amount so he asked Peter to help him. It took Peter and John only 1 day to finish the rest of the job .

Mrs. Lee paid them \$360.00. John and Peter were very happy until they began to divide the money between them.

John said:” I have worked for altogether 7 days but you have worked for only 1 day. Therefore, the total number of days on the job was 8 and we need to divide 8 into \$360 to see how much each of us should be paid per day. ” So John did:

360÷8=\$45.00

John said:” Peter, you worked for only one day, so you should get \$45.00. I worked for 7 days, so the amount I should get is : 45 x 7=\$315.00″

Peter said:” No, You have said that we should be paid according to the amount of work each person did. The first 1/3 of the job was done by you, so you should get: 360 x 1/3=\$120.00 from that. The rest of the job was done by both of us so each one of us should get (360-120) ÷ 2=\$120.00 from 2/3 of the job. Therefore, you should get altogether 120+120=\$240.00.”

John did not agree with Peter so they kept arguing until they saw Mr. Smith, a wise man and a person that they both trust. They presented the problem to Mr. Smith. Mr. Smith thought for a while and said:” Peter should get \$240; John should get \$120.”