Q: Jake and Penny are hunting snakes. Jake's snake is 12 inches longer than Jenny's snake. If the two snakes have a combined length of 70 inches, how long is Jake's snake?
A: Let j be the length of Jake's snake and p be length of Penny's snake. We know that j + p = 70, and j = p + 12. We can substitute the second equation into the first equation to get p + 12 + p = 70. Combining like terms, we get 2p + 12 = 70. Subtracting 12 from both sides, we get 2p = 58. Dividing both sides by 2, we get p = 58 / 2 = 29 inches. Penny's snake is 29 inches. Substituting that length in to the equation j = p + 12, we get j = 29 inches + 12 inches = 41 inches. The answer is 41.
Question: The length of a rectangle is four times its width. If the area is 100 m2. what is the length of the rectangle?
Answer: Let L be the length and W be the width of the rectangle. Hence L = 4 * W. We now use the area to write 80 = L * W. Substitute L by 4 W in the equation above 80 = 4 * W × W = 4 W^2. Solve for W and find L. 4 W^2 = 100. W^2 = 25, W = 5 and. L = 4 * 5 = 20 m. The answer is 20.
[Question]There are 120 cards in a box. If 2/5 of the cards are red, exactly 5/9 of the remainder are black, and the rest are green, calculate the number of green cards in the box?
[Answer]The number of red cards in the box, 2 / 5 of the total number, is 2 / 5 * 120 = 48. The number of cards that are not red is 120 - 48 = 72. If 5 / 9 of the remaining cards are black, then there are 5 / 9 * 72 = 40 black cards in the box. If the remaining cards are green, then there are 72 - 40 = 32 green cards in the box. The answer is 32.
Q: There are 3 workers producing chairs in a furniture factory. Each of them produces 4 chairs an hour. As a group, they produce an additional chair every 6 hours. In total, how many chairs have been produced after 6 hours?
A: The workers produce a combined total of 3 workers * 4 hours = 12 chairs every hour. After 6 hours, they have therefore produced 12 * 6 = 72 chairs. Adding the additional chair means the total amount of chairs produced is 72 + 1 = 73 chairs. The answer is 73.
Question: Vanessa has decided to sell some of her clothes to make pocket money, offering a standard price for each type of item. She made a total of $69 by selling 7 dresses and 4 shirts. If she managed to sell each shirt for $5, how much did the dresses sell for each?
Answer: Let V be the cost of each dress. (7 * V) + (4 * 5) = $69. So, 7 * V + 20 = $69. 7V = $49. V = $49 / 7. V = $7. The answer is 7.
Q: Tommy is making 12 loaves of bread. He needs 4 pounds of flour per loaf. A 10-pound bag of flour costs $10 and a 12-pound bag costs $13. When he is done making his bread, he has no use for flour and so he will throw away whatever is left. How much does he spend on flour if he buys the cheapest flour to get enough?
A:
He needs 48 pounds of flour because 12 x 4 = 48. He needs 4.8 bags of 10 pound bags because 48 / 10 = 4.8. He therefore needs to buy 5 bags of flour because 4 < 4.8 < 5. He spends $50 if he buys this flour because 5 x 10 = 50. He needs 4 bags of the 12 - pound flour because 48 / 12 = 4. He would spend $52 on the 12 - pound bags because 4 x 13 = 52. He spends $50 if he buys the cheapest flour because 50 < 52. The answer is 50.