Q: In the jar, there are 7 blue marbles, 11 red marbles, and some yellow marbles. If the chance of randomly picking a yellow marble is 1/4, how many yellow marbles are there?
A: Let y be the number of yellow marbles. There are 11 + 7 + y = 18 + y total marbles. y / (18 + y) = 1 / 4. 4y = 18 + y. 3y = 18. y = 6. There are 6 yellow marbles. The answer is 6.
Question: On a quiz, Martin answered three fewer questions correctly than Kelsey, and Kelsey answered eight more questions correctly than Campbell. If Campbell answered 35 questions correctly, how many did Martin answer correctly?
Answer: Kelsey answered 35 + 8 = 43 correctly. Martin answered 43 - 3 = 40 correctly. The answer is 40.
[Question]It is recommended that men should consume no more than 150 calories of added sugar per day. Mark took a soft drink in the afternoon that contained 2500 calories, 5% of which was from added sugar. Then he bought some bars of candy which had 25 calories of added sugar each. If he eventually exceeded the recommended intake of added sugar by 100%, how many bars of candy did he take?
[Answer]He consumed 2500 calories, 5% of which is added sugar to give 2500 * (5 / 100) = 125 calories of added sugar. He exceeded the recommended intake of 150 calories by 100% for a total consumption of 150 + (150(100 / 100)) = $300. This means he took in 300 - 125 = 175 calories from candy alone. Each candy had 25 calories so 175 calories which means he consumed 175 / 25 = 7 bars?. The answer is 7.
Q: Emery looks through the drawer where her mom keeps the cookie cutters. There are 6 cookie cutters shaped like triangles, 4 square ones and 2 hexagons. How many sides are there on the cookie cutters in total?
A: The 6 triangles have 3 sides each, for a total of 6 * 3 = 18 sides. The 4 squares have 4 sides each, for a total of 4 * 4 = 16 sides. The 2 hexagons have 6 sides each, for a total of 2 * 6 = 12 sides. The total numbers of sides is 18 + 16 + 12 = 46 sides. The answer is 46.
Question: Twenty years ago, Shane was 2 times older than Garret is now. If Garret is currently 12, how old is Shane now?
Answer: Twenty years ago, Shane was 12 * 2 = 24 years old. Shane is currently 24 + 20 = 44 years old. The answer is 44.
Q: In a car racing competition, Skye drove a 6-kilometer track. For the first 3 kilometers, his speed was 150 kilometers per hour. For the next 2 kilometers, his speed was 50 kilometers per hour more. For the remaining 1 kilometer, his speed was twice as fast as his speed on the first 3 kilometers. What is Skye's average speed for the entire race?
A:
Since time is obtained by dividing distance and speed, then Skye took 3 km / 150 km per hr. = 1 / 50 of an hour to finish the first 3 kilometers of the race. His speed on the next 2 kilometers was 150 + 50 = 200 kilometers per hour. Hence, it took him 2 km / 200 km per hr. = 1 / 100 of an hour to finish the next 2 kilometers. His speed on the remaining 1 kilometer is 150 x 2 = 300 kilometers per hour. Hence, it took him 1 / 300 of an hour to finish the 1 kilometer. So, the total time it took for Skye to complete the race was 1 / 50 + 1 / 100 + 1 / 300 = 1 / 30 of an hour. Therefore, his average speed for the entire race was 6 km / 1 / 30 hour = 180 kilometers per hour. The answer is 180.