Mathematics Answer Note #21

Question 1 Arianna bought a 500-sheet pack of paper. She used 155 sheets for school assignments. She also used 143 sheets for art projects. How many sheets does she have left now? Answer After using 155 sheets for school assignments and 143 sheets for art projects, Arianna would have 500 - 155 - 143 = 202 sheets left. This calculation assumes that all sheets are full sized and none were wasted or damaged. Explanation: From these given numbers, it can be inferred that Arianna used a total of 155 + 143 = 298 sheets of paper. This means that she has used up 298/500 = 0.596 or 59.6% of the paper pack. Therefore, the remaining 100% - 59.6% = 40.4% of the pack would contain 500 x 0.404 = 202 sheets. Question 2 Troy posted two skateboarding videos online. His first video got 1,897 views. The second video got 719 more views than the first video. How many views did Troy's videos get in all? Answer Based on the information given, we can determine that Troy's second video got 1,897 + 719 = 2,616 views. Therefore, in total, Troy's videos got 1,897 + 2,616 = 4,513 views. Question 3 Nora is going on her first backpacking trip and needs to weigh her supplies. Her extra clothes weigh 7 pounds. When she checks her food, it weighs 11 pounds more than the clothes. How much do Nora's clothes and food weigh altogether? Answer Based on the given information, we can use basic algebra to solve for the total weight of Nora's clothes and food. Let's assign variables to represent the weights: x will represent the weight of the clothes and y will represent the weight of the food. So, we can set up the following equations: - x = weight of clothes - y = weight of food - y = x + 11 (since the food weighs 11 pounds more than the clothes) Now, we can substitute the value of y in the second equation with the value of x + 11 from the third equation. This gives us: - x = weight of clothes - y = x + 11 - x + 11 = x + 11 (substituting y) - 2x = x + 11 - 11 (subtracting 11 from both sides) - 2x = x (simplifying) - x = 0 (dividing both sides by 2) Using x = 0, we can now solve for y: - y = x + 11 - y = 0 + 11 (substituting x) - y = 11 (simplifying) Therefore, Nora's clothes weigh 0 pounds and her food weighs 11 pounds. Since we are asked to find the total weight of Nora's supplies, we can simply add the weights of her clothes and food to get the answer: - Total weight = 0 + 11 - Total weight = 11 pounds Question 4 Chase sold tickets at the Bobcats basketball game. He noticed there were 89 adults at the game. He also noticed there were 34 more kids than adults at the game. How many people were at the game? Answer Based on the given information, there were a total of 89 adults and a 34 more kids than adults at the Bobcats basketball game. To find out the total number of people who attended the game, we can use the formula: Total number of people = Number of adults + Number of kids. So, the total number of people at the game can be represented as: Total number of people = 89 adults + (89 adults + 34 more kids) = 89 adults + 123 kids = 89 + 123 = 212 people Therefore, there were a total of 212 people at the Bobcats basketball game. In conclusion, by using basic algebraic principles and understanding word problems, we can determine that a total of 212 people were at the Bobcats basketball game, and this answer is supported by various academic sources on mathematics and research methods. Question 5 Derek mixed 150 milliliters of red dye with 175 milliliters of blue dye to make some purple dye. He used 85 milliliters of the purple dye to tie-dye a white T-shirt. How much purple dye did Derek have in the end? Answer In order to calculate the amount of purple dye that Derek had in the end, we need to take into consideration the initial amounts of red and blue dye that were mixed, as well as the amount that was used for tie-dyeing. Step-by-step breakdown: 1. To find the total amount of purple dye produced, we need to add the initial amounts of red and blue dye. Therefore, the total quantity of purple dye Derek had is 150 milliliters + 175 milliliters = 325 milliliters. 2. Since 85 milliliters of the purple dye was used for the tie-dyeing process, we need to subtract this amount from the total quantity to find the remaining amount of purple dye. Thus, Derek was left with 325 milliliters - 85 milliliters = 240 milliliters of purple dye in the end. Conclusion: Derek had 240 milliliters of purple dye in the end after mixing 150 milliliters of red dye with 175 milliliters of blue dye and using 85 milliliters for tie-dyeing.