6TH GRADE MATH PROBLEMS
By Max Millard
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  1. PERCENTS AND DISCOUNTS
  2. AVERAGES
  3. MULTIPLICATION OF FRACTIONS
  4. Answers

1. PERCENTS AND DISCOUNTS

Toys R Us is having a sale for everything that doesn't move immediately.

If something has been on the shelf for 1 week, it sells for 10% off the original price.

If it's been on the shelf for 2 weeks, the discount is 20% off the original price.

After 3 weeks, it has a 30% discount. After 4 weeks, it's 40% off.

You want to buy a baseball glove, bat and ball.

a. The glove originally cost $80. It has been in the store 2 weeks. How much does it cost now?

b. The bat was originally $20. It has been in the store for 3 weeks. How much it is now?

c. The ball was originally $5. It has been in the store for 4 weeks. What is the price now?

d. What is the total that you need to pay for the 3 items?

e. What if these items had just arrived in the store? What total price would you pay?

f. What if all three items had been in the street for 1 week? How much would the total cost be?


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2. AVERAGES

a. Ming's father promises to buy her a car if she will raise her grades to 90 for the year.

To calculate her grade, her teacher uses the average of three exams that Ming takes during the year. Ming got an 87 on the first exam and an 85 on the second one. What does she need to get on the third one to average 90?


b. David got a 70 in science on his report card. He went to see the teacher to complain about it. His average was 75 before the final exam. The teacher said that the final exam counted for half of the final grade. What grade did David get on the final exam?


c. In Jasmine's Mandarin class, tests count twice as much as quizzes. On the two quizzes she has taken so far, her average grade was 90. What does she need to get on the next test so that she can raise her grade for the class to 95?


d. Henry is very bad at Spanish. He got just 50% of the questions right on the first test, and 60% of the questions right on the second test. What does he need to get on the third test to raise his average score to 70%?


e. Jenny studies karate but isn't very accurate with her kicks. In order to earn her yellow belt, she needs to kick her opponent two out of every three tries. She is allowed 30 tries. If she misses half of her first 12 tries, what fraction of her remaining kicks does she need to connect?


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3. MULTIPLICATION OF FRACTIONS

You visit a fireworks factory and volunteer to help mix the gunpowder. You learn that gunpowder is made up of 10% sulfur, 15% charcoal and 75% saltpeter.

a. What fraction of gunpowder is sulfur?

b. What fraction is charcoal?

c. What fraction is saltpeter?

d. When you are making 1 cup of gunpowder, you accidentally put in 20% sulfur and 65% saltpeter. How much of the other ingredients do you need to add so that the gunpowder will still work?

e. You want to make 100 cups of gunpowder. How many cups of each ingredient do you use?

f. If you want to make 5 cups of gunpowder, how much of each ingredients do you put into the batch?

g. Just to fool around, you make a batch of gunpowder by mixing together 1 cup of each ingredient. You try to explode the batch but nothing happens. What do you add to the mix so that it will have the right percentage of ingredients?

h. You are running short of saltpeter so you decide to substitute salt & pepper. If you are making a 10-gallon batch and you have already put in the right amount of charcoal and sulfur, and half of the saltpeter, how much salt and pepper do you need to add to complete the batch?

i. You mess up and make 8 cups of gunpowder that is 10% charcoal, 15% sulfur and 75% saltpeter. How do you fix the batch without throwing anything away?


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Answers to 6th grade math problems

1. Percents and discounts

a. $64
b. $14
c. $3
d. $81
e. $105
f. $94.50

2. Averages

a. 98
b. 65
c. 100
d. 100
e. 14/18 = 7/9

3. multiplication of fractions

a. 10/100 = 1/10
b. 15/100 = 3/20
c. 75/100 = 3/4
d. 3/20 cups of charcoal, 1/10 + 3/4 cups saltpeter = 17/20 cups
e. 10 cups sulfur, 15 cups charcoal, 75 cups saltpeter
f. sulfur: 1/2 cup. charcoal: 3/4 cup. saltpeter: 3-3/4 cups
g. Make it into 10 cups by adding 1/2 cup charcoal and 6 cups saltpeter.
h. 3-3/4 cups.
i. Make it into 12 cups of gunpowder by adding 1 cup of charcoal and 3 cups of saltpeter.


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