My sister Donna started a trading card collection last year, but unfortunately, she can’t seem to keep track of her cards. Recently she took all of her cards with her on the bus to school. On the way there, some bullying sixth graders stole ¼ of her cards. Then she dropped six cards in the gutter when she got off the bus. She went to class and lost 2/3 of her remaining cards when she passed them around during show-and-tell. Then she gave three cards to her best friend. The teacher, Mr. Purcell, had a stash of trading cards which he let her pick through, giving her enough to increase her total by 1/5. When she went to recess, she found eight cards on the playground. Then at lunch, she accidentally threw half of her remaining cards away in her lunch bag. When she came home, she had only ten cards left. How many cards did Donna have when she left for school?

Question
Asked Nov 13, 2019
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My sister Donna started a trading card collection last year, but unfortunately, she can’t seem to keep track of her cards. Recently she took all of her cards with her on the bus to school. On the way there, some bullying sixth graders stole ¼ of her cards. Then she dropped six cards in the gutter when she got off the bus. She went to class and lost 2/3 of her remaining cards when she passed them around during show-and-tell. Then she gave three cards to her best friend. The teacher, Mr. Purcell, had a stash of trading cards which he let her pick through, giving her enough to increase her total by 1/5. When she went to recess, she found eight cards on the playground. Then at lunch, she accidentally threw half of her remaining cards away in her lunch bag. When she came home, she had only ten cards left. How many cards did Donna have when she left for school?

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Expert Answer

Step 1

If (1/a) of the item is reduced from the lot of x items then remaining items would be equal to x-(x/a)

If (1/a) of the item is added to the lot of x items then remaining items would be equal to x+(x/a)

reduced
x
a
added
a
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reduced x a added a

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Step 2

Donna came home with 10 cards. Assume she had p cards when she lost (1/2) of them in her lunch bag.

So,

р
10%3D р-
2
10- р
2
р3 20
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р 10%3D р- 2 10- р 2 р3 20

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Step 3

Out of them she got 8 on the playground. So, the number of c...

20 q8
q20-8
12
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20 q8 q20-8 12

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