Math 0306 - Lab Assignment Week 4 - Answers
The problems are available at
In case you have some trouble reading the page
÷ is a division sign * is a multiplication sign
1. Sally's Birthday
let x be the number of Sally's classmates1/2 * 1/3 * x = 4
1/6 x = 4
x = 4 * 6 = 24
OR 1/3 of the kids at the party brought 4 gifts. Therefore 12 kids are at the party. These 12 kids are 1/2 of her classmates. Therefore she has 24 classmates.
2. Shipping Packages
3/4 of the packages have to wait3/4 * 272 = 204 packages have to wait.
3. Happy Campers
1/4 of the campsites are still open.1/4 * 128 = 32 campsites are still open.
You tried to reserve at least 33 sites.
4. Magic Square
Bottom row: 1/5 + 7/10 + 3/5 = 2/10 + 7/10 + 6/10 = 15/10 (= 5/3 but this is no advantage here)Therefore first row: x + 3/10 + 8/10 = 15/10 so x = 4/10 = 2/5
Second row: 9/10 + 1/2 + x = 15/10 so x = 15/10 - 9/10 - 5/10 = 1/10
The product of the missing fractions = 2/5 * 1/10 = 1/25
5. Richard's Garden
carrot bed: 8 sq mradish bed is half of the carrot bed: 4 sq m
tomato bed is half of the radish bed: 2 sq m
total area: 14 sq m
6. The Highway Department
The remaining 46 miles of roads are 1/4 of the roads (1 - 1/4 - 2/4).The total length of the roads is therefore 46 ÷ 1/4 = 46 * 4 = 184 miles.
7. Handicapped Entrances
1/3 of 1800 public buildings do not have handicapped entrances.1/3 * 1800 = 600 buildings
A fine of $ 3000 each: 600 * 3000 = $1,800,000
8. Bad Day for Sixth Grade
Students who came to school: 1/2 * 360 = 180Students who came on time: 1/2 * 180 = 90
Students who were dry: 1/2 * 90 = 45
9. Fraction Triangle
The three sides of the triangle read:3/3 1/6 5/6
3/3 1/3 2/3
5/6 1/2 2/3
10. Ms. William's Test Results
The fraction is 1/1 or 24/24 (assuming 24 students)
11. Xynco School
The students who voted can be calculated by adding all the fractions:2/7 + 1/7 + 1/14 + 1/7 + 1/56 + 1/28 + 1/7 + 1/28 + 1/14 + 1/28 + 1/112 =
32/112 + 16/112 + 8/112 + 16/112 + 2/112 + 4/112 + 16/112 + 4/112 + 8/112 + 4/112 + 1/112 = 111/112
The remaining 1/112 are the 16 absent students. Therefore the total school population is
16 ÷ 1/112 = 16 * 112 = 1792 students.
12.Spring Fling
Tickets remaining after first day: 1/2Tickets remaining after second day 1/2 * 1/2 = 1/4
Tickets remaining after third day 1/4 * 2/3 = 1/6
1/6 of the tickets = 2000
Total tickets = 2000 ÷ 1/6 = 2000 * 6 = 12000
13. Big Numerator and Denominator
1/3 + 6/9
14. Sailors and Coconuts
This one is best started at the end. The first thing you need to realize is that the amount left by each sailor after he divides the coconuts is even because he groups 2 sailor's shares. So the amount left in the morning is an even number. After the monkey gets his coconut, the number is odd. Any odd number divided by 3 (the three sailors) is also odd. Therefore each sailor gets an odd number of coconuts.1. Trial: Assumption: Each sailor gets one coconut, which means 4 coconuts were left in the morning (1 for each sailor and 1 for the monkey). This means when Carl divided up the shares, everyone had 2 coconuts, so before Carl starts dividing there were 7 coconuts ( 2 for each sailor, 1 for the monkey). As we have seen earlier, an odd number could not have been left by Bob.
2. Trial: Assumption: Each sailor gets three coconuts, which means 10 coconuts were left in the morning (3 for each sailor and 1 for the monkey). This means when Carl divided up the shares, everyone had 5 coconuts, so before Carl starts dividing there were 16 coconuts ( 5 for each sailor, 1 for the monkey). This means when Bob divided up the shares, everyone had 8 coconuts, so before Bob starts dividing there were 25 coconuts ( 8 for each sailor, 1 for the monkey). As we have seen earlier, an odd number could not have been left by Mark.
3. Trial: Assumption: Each sailor gets five coconuts, which means 16 coconuts were left in the morning (5 for each sailor and 1 for the monkey). This means when Carl divided up the shares, everyone had 8 coconuts, so before Carl starts dividing there were 25 coconuts ( 5 for each sailor, 1 for the monkey). As we have seen earlier, an odd number could not have been left by Bob.
4. Trial: Assumption: Each sailor gets seven coconuts, which means 22 coconuts were left in the morning (7 for each sailor and 1 for the monkey). This means when Carl divided up the shares, everyone had 11 coconuts, so before Carl starts dividing there were 34 coconuts (11 for each sailor, 1 for the monkey). This means when Bob divided up the shares, everyone had 17 coconuts, so before Bob starts dividing there were 52 coconuts ( 17 for each sailor, 1 for the monkey). This means when Mark divided up the shares, everyone had 26 coconuts, so before Mark starts dividing there were 79 coconuts ( 26 for each sailor, 1 for the monkey). The minimum number of coconuts the sailors found were 79.
15. Fleadirt Gang
This is another one of the problems you solve best by starting at the end. After meeting the third Fleadirt, the boy has 2 golf balls left. He gave Fleadirt 2 balls plus his other half, which is 4 balls ( 2+2). Before meeting the third, after meeting the second, Fleadirt, he had therefore 8 balls ( 4*2). He gave the second Fleadirt 2 balls plus the other half, which is 10 balls ( 8+2). Before meeting the second, after meeting the first, Fleadirt, he had therefore 20 balls (10*2). He gave the first Fleadirt 2 balls plus the other half, which is 22 balls (20+2). He therefore started with 44 balls (22*2)
16. Mr. Thomas' Bulbs
This spring's 170 bulbs are 1/3 of last year's bulbs, so last years bulbs equal170 ÷ 1/3 = 170 * 3 = 510 bulbs. The total bulbs for both years are 170 + 510 = 680 bulbs.
17. Days in One-Fifth of a Year
1/5 of a year equals 1/5 * 365 = 73 days.
18. Kitchen Matches
Ms. Horton has used 3/4 of the matches, which is500 * 3/4 = 375.
She started using matches from this box 375 days ago.
19. Newt Scouts
Martin, Santiana and Harold contributed 1/4 + 1/8 + 3/12 = 6/24 + 3/24 + 6/24 = 15/24 = 5/8.Maurice contributed the remaining of the tickets or 12 tickets. The total number of tickets is
12 ÷ 3/8 = 12 * 8/3 = 32 tickets
20. Ratio of Water to Wine
After each step, 36/45 or 4/5 of the wine remains in the cask.After two steps, the ratio becomes 4/5 * 4/5 = 16/25