Math Challenge 5
Solutions
1.
I ate 2 cookies. Ben ate twice as many cookies as I ate. How many cookies did we eat
altogether?
Answer: 6
Jay has 6 baseball cards. John has 4 times as many baseball cards as Jay. How many
baseball cards does John have?
Answer: 24
Doug has $7. Sam has three times as much money as Doug. How much money does Sam
have?
Answer: $21
4.
Ella worked 45 hours. That was 9 times as many hours as Juan worked. How many hours
did Juan work?
Answer: 5 [hours]
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5.
When Sanika multiplies her age by two, and multiplies it again by two, she gets 28. How
old is Sanika?
Answer: 7
Tommy has 6 times as many action figures as Henry. Henry has 11 action figures. How
many action figures do they have altogether?
Answer: 77
Lily and Julian run the Solve It Detective Agency. Lily solved 56 mysteries. That was 7 times
as many mysteries as Julian solved. How many fewer mysteries did Julian solve than Lily?
Answer: 48
Eric and Cole sold 48 buttons altogether. Cole sold 3 times as many buttons as Eric. How
many buttons did Eric sell?
Answer: 12
Chloe read 9 times as many books as Jason. Together, they read a total of 120 books. How
many books did Chloe read?
Answer: 108
2.
3.
6.
7.
8.
9.
Jason
Chloe
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10 units = 120, so 1 unit = 12
Jason = 1 unit = 12; Chloe = 9 units = 12 x 9 = 108
10. Together, Lisa and Lena have 104 Wii games in their collection. Lisa collected 7 times as
many Wii games as Lena. How many more Wii games does Lisa have than her sister?
Lena
Lisa
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Answer: 78
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8 units = 104, so 1 unit = 104 ÷8 = 13
Lena = 1 unit = 13; Lisa = 104 – 13 = 91
Lisa has 91-13 = 78 more games than her sister
11. The sum of two numbers is 260. One number is 9 times as big as the other. What is the
bigger number? (similar strategy with problem 8)
Answer: 234
12. Tia can solve 105 math problems in 34 minutes and 30 seconds. Tina can solve the same
105 math problems in twice Tia’s time. Tom can solve the same 105 math problems in 20
minutes and 30 seconds faster than Tina. How long, in minutes, will it take Tom to solve
the 105 math problems?
Answer: 48 min 30 sec
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Tina’s: 2 x (34 min and 30 sec) = 69 minutes. Tom’s: 69 min – 20 min 30 sec = 48 min 30 sec
2015-2016 Math Challenge
13. Jack has 2 blue candies for every 1 green candy. After he eats 1 of the blues and 2 of the
green, Jack has 5 blues candies for every 2 green candies. How many candies does Jack
start with? Hint: make a table for Before and After.
Before eating the 3 candies
Answer: 24 candies
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After eating the 3 candies
Blue
2
4
6
…
14
16
18
20
Blue-1
1
3
5
…
13
15
17
19
Green
1
2
3
…
7
8
9
10
Green-2
--
0
1
…
5
6
7
8
Notice that only 15 and 6 can represent 5 blues for every 2 greens.
Jack ends with 15 blue and 6 green candies, which is 5 blues for every 2 greens. Then Jack must start with 16
blues and 8 green for a total of 24 candies.
14. At Kids Academy, 9 times as many children signed up for swimming as science. If 52
children switch from swimming to science, there will be an equal number of children in
each class. How many children are there altogether? Hint: make a table for Before and
After.
Before 52 children switch from swimming to
science
Answer: 130
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After 52 children switch from swimming to
science
Swimming
90
99
108
117
126
135
…
Swimming -52
38
47
56
65
74
83
Scitence
10
11
12
13
14
15
…
Science +52
62
63
64
65
66
67
Notice that on the fourth guess, after 52 moved to science from swimming, there are 65 students in swimming
and 65 students in science.
Math Challenge 6 will be available online December 18, 2015 at www.mathinaction.org.
2015-2016 Math Challenge