ACE Project 3
p. 43 (15, 24, 28, 30, 34, 39)
15)The school cafeteria serves pizza every sixth day and
applesauce every eighth day. If pizza and applesauce are
both on today’s menu, in how many days will they be
together on the menu again?
6
12
18
8
16
24
24
• In 24 days they will be together on the menu
again.
24) For which pair is the greatest
common factor 8?
• A – 2 and 4
2:
1
2
4:
1
2
• B – 7 and 15
7:
1
7
15:
1
3
• C – 32 and 64
• D – 56 and 72
4
5
15
32:
1
2
4
8
16
32
64:
1
2
4
8
16
32
56:
1
2
4
7
8
14
28
56
72:
1
2
3
4
6
8
9
12
64
18
24
36
72
28) The cast of a play had a party at the drama teacher’s house. There were
20 cookies and 40 carrot sticks served as refreshments. Each cast member
had the same number of whole cookies and the same number of whole carrot
sticks. Nothing was left over. The drama teacher did not eat. How many cast
members might have been at the party? Explain.
20:
1
2
4
5
10
20
40:
1
2
4
5
8
10
20
40
• There could have been 1, 2, 4, 5, 10 or 20 cast
members at the party. I know this because 1, 2,
4, 5, 10 and 20 are common factors of 20 and
40.
30) Neena has 54 smiley-face stickers, 36 glittery stickers,
and 81 heart stickers. She wants to divide the stickers
evenly among her friends. Find the greatest number that
Neena can use to divide the stickers evenly.
54:
1
2
3
6
9
18
27
54
36:
1
2
3
4
6
9
12
18
81:
1
3
9
27
81
• G–9
36
34a) Suppose a jet travels 60 kilometers in 5
minutes. How many kilometers will it travel in 2
hours? In 6 hours?
• 60 minutes in a hour so 120 minutes in 2 hours
(60 * 2)
• 120 min ÷ 5 = 24 sets of 5 minute intervals
• 24(60 km) = 1440 kilometers
• In 2 hours the jet will travel 1440 kilometers.
• 60 minutes in a hour so 360 minutes in 6 hours
(60 * 6)
• 360 min ÷ 5 = 72 sets of 5 minute intervals
• 72(60 km) = 4320 kilometers
• In 6 hours the jet will travel 4320 kilometers.
34b) How many more kilometers will the jet travel in 6
hours than in 2 hours?
• In grading this question I read along with your
answer to Part A.
• 4320 km – 1440 km = 2880 kilometers
• The jet will travel 2880 kilometers more in 6
hours than in 2 hours.
34c) Suppose that Nodin flew on this jet to
the Dominican Republic. If his trip took 4
hours, how many kilometers did he travel?
Option 1
Option 2
• 60 minutes in a hour so 240
minutes in 4 hours (60 * 4)
• 240 ÷ 5 = 48 sets of 5 minute
intervals
• 48(60 km) = 2880 km
• Nodin will travel 2880
kilometers.
• In part B you found the
difference between the 6 hour
flight and the 2 hour flight.
• This is equivalent to a 4 hour
flight.
• Therefore, your answer to part
B and part C should be
equivalent.
39) Suppose that in some distant part of the universe, there is a star
with four orbiting planets. One planet makes a trip around the star in
6 Earth years, the second planet takes 9 Earth years, the third takes
15 Earth years, and the fourth takes 18 Earth years. Suppose that at
some time the planets are lined up as pictured below. This
phenomenon is called conjunction. How many years will it take before
the planets return to this position?
6
12
18
24
30
36
42
48
54
60
9
18
27
36
45
54
63
72
81
90
15
30
45
60
75
90
18
36
54
72
90
66
72
78
84
90
• In 90 Earth years the planets will return to this
position.