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question:Jason is counting the number of cars that drive by his window. He counted four times as many green cars as red cars, and 6 more red cars than purple cars. If he counted 312 cars total, how many of them were purple?

answer:Let's start by assigning variables to the unknowns. Let's say the number of purple cars is P. According to the information given, there are 6 more red cars than purple cars, so the number of red cars is P + 6. And there are four times as many green cars as red cars, so the number of green cars is 4*(P + 6). The total number of cars is given as 312, so we can write the equation: P + (P + 6) + 4*(P + 6) = 312. Simplifying the equation, we get: P + P + 6 + 4P + 24 = 312. Combining like terms, we get: 6P + 30 = 312. Subtracting 30 from both sides of the equation, we get: 6P = 282. Dividing both sides of the equation by 6, we get: P = 47. Therefore, there were 47 purple cars. 47 The answer is: 47

question:Tina decides to fill a jar with coins. In the first hour she puts in 20 coins. During the next two hours she puts in 30 coins each time. During the fourth hour she puts in 40 coins. During the fifth hour her mother asks to borrow some money so she takes x coins out. How many coins are left after the fifth hour? If we know the answer to the above question is 100, what is the value of unknown variable x?

answer:In the first hour, Tina puts in 20 coins. During the next two hours, she puts in a total of 30 coins each time, so she puts in 2 * 30 = 60 coins. During the fourth hour, she puts in 40 coins. So far, she has put in a total of 20 + 60 + 40 = 120 coins. During the fifth hour, Tina takes out x coins. The number of coins left after the fifth hour is 120 - x. We are given that the number of coins left is 100, so we can write: 120 - x = 100. Solving for x, we get: x = 20. The value of x is 20. 20 The answer is: 20

question:f the marching band has a total of 110 members and there are four times as many percussion players as there are woodwind players, and twice as many woodwind players as brass players, how many brass players are there in the marching band?

answer:Let's assume the number of brass players is B. Then the number of woodwind players is 2B, since there are twice as many woodwind players as brass players. And the number of percussion players is 4 * 2B = 8B, since there are four times as many percussion players as there are woodwind players. The total number of members in the marching band is B + 2B + 8B = 11B. Given that the total number of members is 110, we can set up the equation 11B = 110. Solving for B, we find that B = 10. Therefore, there are 10 brass players in the marching band. 10 The answer is: 10

question:What value of x makes the equation below true: 2x + 4 = |{-17 + X If we know the answer to the above question is 5, what is the value of unknown variable X?

answer:We want to find the value of X in the given equation. The equation is: 2x + 4 = |{-17 + X}| To solve for X, we can start by isolating the absolute value expression by subtracting 4 from both sides of the equation: 2x = |{-17 + X}| - 4 Now, we can consider the two possible cases for the absolute value expression. Case 1: -17 + X is positive or zero In this case, the absolute value expression simplifies to -17 + X. So, we can rewrite the equation as: 2x = -17 + X - 4 Simplifying, we have: 2x = X -21 Subtracting X from both sides of the equation, we find: 2x - X = -21 x = -21 However, since we are looking for a positive value of x, this solution is not valid for this case. Case 2: -17 + X is negative In this case, the absolute value expression simplifies to -(-17 + X), which is equal to 17 - X. So, we can rewrite the equation as: 2x = 17 - X - 4 Simplifying, we have: 2x = 17 - X - 4 2x = 13 - X Adding X to both sides of the equation, we find: 2x + X = 13 3x = 13 Dividing both sides of the equation by 3, we get: x = frac{13}{3} Given that the value of x is 5, we can substitute it into the equation: 5 = frac{13}{3} This equation does not hold true, so the solution for this case is also not valid. Since neither case provides a valid solution, we can conclude that there is no value of X that makes the equation true. The answer is: 3