Mathacle. PSet Algebra, Ratios Level Number Name: Date: Solve.

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1 Solve. 1.) Eight students play a game that lasts for 80 minutes, but only allows 5 students to play at a time. If each of the eight students plays the same length of time throughout the game, how many minutes does each student play? 2.) At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party? 3.) A grocer puts 18 apples in N bags such that each bag contains the same number of apples. If there is more than one apple and fewer than 18 apples in each bag, what are the possible values of N?

2 4.) Tom has a 1/3 more money than what Jessica has. If Tom gives $9 to Jessica, she will have a 4/5 more money than what Tom has. How much money does each one have initially? 5.) The ratio of numbers of chicken to pig is 26:5; the ratio of the numbers of sheep to horse is 25:9; the ratio of numbers of pig to horse is 10:3. What is the ratio of the numbers of chicken to pigs to horse to sheep? 6.) If a : b = 21: 4, and a : c = 7 : 6. What is a : b : c? 7.) The total weight of three fruit baskets is 60 grams. If 3 grams of the fruit is removed from the first basket and second basket, respectively, and put into the third basket, the ratio of the weights of the three baskets is1: 2 : 3. Find the original weight of each basket.

3 8.) A school group charters three identical buses and occupies 4/5 of the seats. After ¼ of the passengers leave, the remaining passengers use only two of the buses. What fraction of the seats on the two buses is now occupies? 9.) Jason has twice as many red marbles as blue marbles. He puts then in two jars in such a way that the ratio of the number of red marbles to the number of blue marbles in jar I is 2:7 and there are only red marbles in jar II. The number of red marbles in jar II is how many times the number of red marbles in jar I? 10.) A number of people boarded a bus at the terminal. At the first stop, half of the passengers got off and one got on. At the second stop, 1/3 of passengers on the bus got off and one got on. If the bus then had 15 passengers, how many were there when the bus left terminal?

4 11.) Vlatko has a bag that holds only green marbles and red marbles. The ratio of green marbles to total number of marbles in the bag is 2/5. If Vlatko adds 4 green marbles and takes out 10 red marbles, there will be twice as many green marbles in the bag as red marbles. How many marbles were in the original bag? 12.) What is the ration of x to y if 10x 3y 13x 2y 3 = 5 13.) If x y 2 = and 3 y z 7 = 5, then what is x z? 14.) The ratio of men to women in Smalltown is 3:2. The population of Bigtwon is three times as large as that of Smalltown, and the ratio of men to women in Bigtown is 2:3. If Smalltown and Bigtowm are combined, what is the ratio of men to women in the combination?

5 15.) My piggy bank has only pennies and nickels in it, and 2/7 of the coins are nickels. If I remove 84 pennies, then 1/3 of the remaining coins are pennies. a.) Suppose there are initially p pennies and n nickels in the piggy bank. Write an equation using the fact that 2/7 of the coins initially in the piggy bank are nickels. b.) Write a second equation representing the situation after 84 pennies are removed. c.) How many nickels are in the piggy bank? 16.) My baseball team won 2/9 of its games this reason. If we lost 15 more games than we won, how many games did we play this year? 17.) If a 3 = b 4 and a = c 5 b, what is? c

6 18.) Joe and JoAnn each bought 12 ounces of coffee in a 16-ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe s coffee to that in JoAnn s coffee? 19.) Gregor is planting pea plants in his backyard. Some of the plants are tall and the rest are short. Some of the plants are yellow and the rest are green. THe numbers of different plant types are in ratio Tall green: Tall yellow : Short green : Short yellow = 8 : 5 : 2 : 1 If there are 1080 green plants, the how many total plants are in Gregor s yeard? 20.) In recent election for mayor, there were three candidates, Smith, Williams, and Krzyzewski. The ratio of Krzyzewski voters to Smith voters is the same as the ratio of Smith voters to Williams voters. If there are 800 Krzyzewski voters and 200 Williams voters in my town, how many people voted in my town ( assuming these were the only 3 choices)?

7 21.) Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio 3:2:1, respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of candy, what fraction of the candy goes unclaimed? 22.) [AMC12 A, 2002, #10] Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What is fraction of the liquid in the first cup is now cream?