Question: Three times the sum of marbles that Atticus, Jensen, and Cruz have is equal to 60. If Atticus has half as many marbles as Jensen, and Atticus has 4 marbles, how many marbles does Cruz have?
Answer: Three times the sum of marbles that Atticus, Jensen, and Cruz have is equal to 60, meaning together they have 60 / 3 = 20 marbles. If Atticus has half as many marbles as Jensen, and Atticus has four marbles, Jensen has 2 * 4 = 8 marbles. Together, Atticus and Jensen have 8 + 4 = 12 marbles. Since the sum of marbles that Atticus, Jensen, and Cruz have is equal to 20, and Atticus and Jensen have 12 marbles, Cruz has 20 - 12 = 8 marbles. The answer is 8.
[Question]Candace decides to enter a race. The race is run in 4 segments, with racers eliminated at the end of each segment. 10 racers are eliminated after the first segment. A third of the remaining racers are eliminated after the next section. Half of the remaining racers are eliminated before the last leg of the race. If 100 racers started the race, how many will run in the final section of the race?
[Answer]After the first segment, there are 100 – 10 = 90 racers left in the race. After the second segment, 90 / 3 = 30 racers are eliminated. This leaves 90 – 30 = 60 racers to compete in the third segment. After the third segment, 60 / 2 = 30 more racers are eliminated. This leaves 60 – 30 = 30 racers to run in the final section of the race. The answer is 30.
Q: All 20 of Grant’s baby teeth have fallen out and he has a total of $54 from the tooth fairy. Every time he lost a tooth, he put it under his pillow for the tooth fairy, except for one that he dropped on the way home from school and another he swallowed accidentally. The tooth fairy left Grant $20 when he lost his first tooth. How much did the tooth fairy leave him per tooth after his first tooth, assuming equal money exchanged for each tooth thereafter?
A: Grant’s 20 baby teeth – 1 tooth he dropped – 1 he swallowed = 18 teeth left for the tooth fairy. We aren’t counting his first tooth, so 18 teeth – 1 first tooth = 17 teeth. Grant received $54 - $20 = $34 in total for all the teeth after the first. So he received $34 / 17 teeth = $2 for each tooth after his first tooth. The answer is 2.
Question: Thomas buys a weight vest. It weighed 60 pounds and worked well for him in the beginning but after a bit of training he decides he wants to increase the weight by 60%. The weights come in 2-pound steel ingots. Each ingot cost $5 and if you buy more than 10 you get a 20% discount. How much does it cost to get the weight he needs?
Answer: He needs to buy 60 * .6 = 36 pounds. So he needs to buy 36 / 2 = 18 weight plates. That would cost 18 * 5 = $90. Since he bought more than 10 he gets a discount so he gets 90 * .2 = $18 off. That means he paid 90 - 18 = $72. The answer is 72.
[Question]In a batch of 30 apples, 1/6 are too small and 1/3 are not ripe. The others are perfect. Calculate the number of perfect apples.
[Answer]We first calculate the proportion of all the other apples: 1 / 6 + 1 / 4 + 1 / 12 = 2 / 12 + 3 / 12 + 1 / 12 = 6 / 12. So, the proportion of perfect apples is 12 / 12 - 6 / 12 = 6 / 12 = 0.5. Thus the number of perfect apples is 0.5 * 30 = 15. The answer is 15.
[Question]Anna has 3 times as many toys as Mandy and 2 fewer toys than Amanda. If they have 142 toys all together, how many toys does Mandy have?
[Answer]
Let x be the number of toys Mandy has. Anna has 3 * x toys. Amanda has 3 * x + 2 toys. x + 3 * x + 3 * x + 2 = 142. 7 * x + 2 = 142. 7 * x = 140. x = 20. The answer is 20.