Math 123
Fractions problem solving
1. The students in the Douglas School have left for their annual school trip. One-third of the students went to Washington D.C. One-third of them went to Annapolis. One-fourth of them went to Williamsburg, and the remaining 100 students went to Monticello. How many students are in the class? How many went to each place?
2. David and Mike went fishing. David brought 5 hoagie sandwiches and Mike brought 3 hoagie sandwiches. As they were getting ready to eat, their friend, Jerry, joined them. However, Jerry did not bring any hoagies with him. After lunch, during which the three men shared the 8 hoagies equally, Jerry put down 8 coins of equal value to pay for his share of the lunch. How should David and Mike share the 8 coins?
3. One jar is half full of vinegar and another jar twice its size is one quarter full of vinegar. Both jars are filled with water and the contents are mixed in a third container. What part of the mixture is vinegar?
4. At school they did a survey of everyone's favorite sport. The survey showed that one third as many kids liked tennis as liked basketball. There were one fifth as many kids who said they liked basketball as said they liked baseball or softball. Then one half as many kids liked baseball or softball as liked soccer. There were 90 kids who liked soccer the best. How many kids did they interview, and how many liked each sport the best?
5. With the spring dance coming up, the dance committee did a survey to see what kind of band to get. They talked to 123 students and found that twice as many people wanted soul music as jazz; the number wanting heavy metal was 2/7 as many as the number wanting rock; 1/2 as many wanted the big band sound as heavy metal; 1/3 the combined total of jazz and soul wanted country western; 5 more than the combined total for jazz, country western, and soul wanted rock; and there were 2 fewer votes for reggae than jazz. How many votes did each band get?
6. Put one of the fractions 1/12, 1/6, 1/4, 5/12, 1/2, 7/12, 3/4, 5/6, and 11/12 in each of the boxes of a 3x3 grid so that the sum of the fractions in each row and column is 3/2.
7. The numerator and denominator of a fraction are in the ratio of 3:4. If 1 is subtracted from the numerator and 2 is added to the denominator, the value of the resulting fraction is equal to 2/3. Find the original fraction.
8. A man spent 1/3 of his money and then lost 2/3 of the remainder. He was left with $12.00. How much did he start with?