| Problem |
Solution |
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1) Jason is playing with a stack of cards. He divides the cards into 3 equal piles. Then he takes one
pile and divides it into 4 equal piles. Then he takes one of the four equally divided piles and further
divides it into 5 equal piles. If one of the five equally divided piles contains 3 cards, how many
cards in total are in Jason's stack? |
Work this problem backwards:
1. If Jason has 5 piles at the end and each pile contains 3 cards then those 5 piles contain 15 cards total.
2. If those 5 piles were 1/4 of the cards in the previous step,then the 4 piles together contain 60 cards.
3. Those 4 piles are 1/3 of the deck, so the whole deck contained 180 cards.
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2) The sum of two numbers is 22 and their product is 96. What is the ratio of the two numbers when
expressed as a proper fraction in lowest terms? |
1. Write out the 2 number factors of 96:
32 x 3 16 x 6 8 x 12 4 x 24 2 x 48
2. Find the two that sum to 22 = 16 and 6.
3. Express the ratio of these two numbers =
6/16 = 3/8
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3) What is the greatest common prime factor of 78 and 117? |
1. Write out the prime factors of both numbers.
factors of 78 = 39 x 2 = 13 x 3 x 2
factors of 117 = 39 x 3 = 13 x 3 x 3
2. The largest one in both lists = 13
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4) A costume store has a sale. All costumes are being sold at a discount and are 25% off the original
price. One costume has a tag that marks it for an additional 10% off the discounted price. If the
original price of the costume is $50, what is the final sale price (not including tax)?
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1. The discount price is $50 - 25% of 50 =
$50 - $12.50 = $37.50
2. A further discount of 10% off this price is $3.75.
3. Subtract this from the first discount price to get the final sale price = $37.50 - $3.75 = $33.75
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5) A group of children are picking apples in an orchard. Kyle collects 28 apples, Rachel collects 33
apples, Lima collects 39 apples in a day. They want to make $200 for a trip they are planning. If
they get $2 for every 25 apples picked, how many days will they need to pick apples to make
enough money for their trip? |
1. What is the total number of apples picked in a day by all kids? = 28 + 33 + 39 = 100 apples
2. Divide this by 25 = 100 apples/25 = 4.
3. Multiply by $2 to get the amount the kids get paid per day = 4 x $2 = $8 per day.
4. Divide the cost of the trip by this amount to get the number of days = $200/$8 = 25 days
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