Question: The cheerleading coach is ordering new uniforms. There are 4 cheerleaders who need a size 2, a certain number who need a size 6, and half that number who need a size 12. If there are 19 cheerleaders total, how many cheerleaders need a size 6?
Answer: Let s be the number of cheerleaders who need a size 6 and t be the number who need a size 12. We know that s = 2t and s + t + 4 = 19. Substituting the first equation into the second equation, we get 2t + t + 4 = 19. Combining like terms, we get 3t + 4 = 19. Subtracting 4 from both sides, we get 3t = 15. Dividing both sides by 3, we get t = 5. Substituting that value back into the equation s = 2t, we get s = 2 * 5 = 10. The answer is 10.
[Question]Paul's grades last semester were very bad. To encourage him, Paul's dad promised him $5 for every B+ he gets in his next scorecard and twice that amount for every A. If Paul obtains at least two A+ he'll double the previous rewards and would receive a flat $15 for every A+ obtained (with no extra bonus). If there are 10 courses with grades in Paul's scorecard, what's the maximum amount he could receive from his dad?
[Answer]We know Paul would get $5 for a B + . However, we know this could be (2x) doubled if he obtains at least two A + . This means 2 * $5 = $10 for a B + if Paul gets at least two A + . We know Paul would get twice the reward of a B + if he gets an A. This means 2 * $5 = $10 for every A. However, we know his reward for every A could be (2x) doubled if he obtains at least two A + . This means 2 * $10 = $20 for every A if Paul gets at least two A + . We learn here then that Paul will get a higher reward for obtaining A grades ($20) than getting A + grades ($15) as long as he's able to score at least two A + . To maximize his payout, Paul will need to get only (2) two A + from his 10 courses. Therefore he should aim to get an A in the remaining 10 - 2 = 8 courses. Assuming Paul can get two A + and eight A in his next scorecard his total payout would be 2 * $15 + 8 * $20. This translates into $30 + $160 or $190. The answer is 190.
Q: Harrison Elementary School is overcrowded with 1590 students, so 40% of the students are going to move to a new school. There are 3 grade levels, and each grade level needs one 20-person advanced class and the rest of the students divided evenly into 6 additional classes. How many students will there be in each normal class at the new school?
A: First find how many students go to the new school: 1590 students * .4 = 636 students. Then divide that number by 3 to find how many students are at each grade level: 636 students / 3 grades = 212 students / grade. Then subtract the 20 students in the gifted class: 212 students - 20 students = 192 students. Then divide that number by 6 to find the number of students in each other class: 192 students / 6 classes = 32 students / class. The answer is 32.
Question: A particular train has some passenger cars and a number of cargo cars equal to half the number of passenger cars plus three. If the total number of cars is 71, counting the engine and caboose, how many passenger cars are in the train?
Answer: First find the number of cars not counting the engine and caboose: 71 cars - 2 cars = 69 cars. Let p be the number of passenger cars and c be the number of cargo cars. We know that p + c = 69 and c = p / 2 + 3. Substituting the second equation into the first, we get p + p / 2 + 3 = 69. Combining like terms, we get 1.5p + 3 = 69. Subtracting 3 from both sides, we get 1.5p = 66. Dividing both sides by 1.5, we get p = 44. The answer is 44.
[Question]Scout delivers groceries on the weekends. His base pay is $10.00 an hour. He also earns a $5.00 tip per customer that he delivers groceries to. On Saturday he worked 4 hours and delivered groceries to 5 people. Sunday he worked 5 hours and delivered groceries to 8 people. How much did he make over the weekend?
[Answer]He worked 4 hours on Saturday and 5 hours on Sunday for a total of 4 + 5 = 9 hours. His base pay is $10.00 an hour and he worked 9 hours for a total of 10 * 9 = $90.00. He delivered groceries to 5 people on Saturday and 8 people on Sunday for a total of 5 + 8 = 13 deliveries. He makes $5.00 per delivery and he delivered to 13 people so he made 5 * 13 = $65.00. His base pay is $90.00 and he made $65.00 in tips for a total of 90 + 65 = $155.00. The answer is 155.
[Question]Michonne is inviting her friends to her birthday party. She invites 6 of her friends from school and 12 of her friends from her neighborhood. Each of her friends asks if they can bring two friends along as well. How many people are going to Michonne's birthday party?
[Answer]
Michonne has invited 6 + 12 = 18 friends. These friends have invited another 18 friends * 2 = 36 people. So in total, there are 18 friends + 36 people = 54 people going to Michonne's party. The answer is 54.