[Question]In ancient China, soldiers positioned in beacon towers along the Great Wall would send smoke signals to warn of impending attacks. Since the towers were located at 5 kilometer intervals, they could send a signal the length of the Great Wall. If the Great wall was 7300 kilometers long, and every tower had two soldiers, what was the combined number of soldiers in beacon towers on the Great Wall?
[Answer]If there were beacon towers every 5 kilometers along the 7300 kilometer length of the Great Wall, then there were 7300 / 5 = 1460 beacon towers. If every tower had two soldiers, then there were a total of 1460 * 2 = 2920 soldiers in beacon towers along the Great Wall. The answer is 2920.
Q: The school has 14 boys and 10 girls. If 4 boys and 3 girls drop out, how many boys and girls are left?
A: There are 14 boys - 4 boys = 10 boys left. There are 10 girls - 3 girls = 7 girls left. In total there are 10 boys + 7 girls = 17 boys and girls left. The answer is 17.
Question: At the bake sale, Tamara makes $32 from the brownies. She made 2 pans of brownies which were all sold. The brownies were cut into 8 big square pieces. How much did each brownie cost?
Answer: Tamara had 2 x 8 = 16 big square brownie pieces. Each brownie piece cost $32 / 16 = $2. The answer is 2.
[Question]Mark deposited $88 in a bank. Bryan deposited $40 less than five times as much as Mark. How much did Mark deposit in the bank?
[Answer]Five times the amount Mark deposited is $88 x 5 = $440. So, Mark deposited $440 - $40 = $400. The answer is 400.
Q: Karen's students are about to take a standardized test. Karen gets a $500 bonus if their average score is above 75, plus an extra $10 bonus for every additional point the average score increases above 75. So far, Karen has graded 8 tests, and the average is 70. Given that each student can have a maximum score of 150, what combined score do the last two tests need to have for Karen to earn a $600 bonus?
A: First subtract $500 from Karen's goal bonus amount to find how much she makes from the extra $10 / point bonus: $600 - $500 = $100. Then divide the extra bonus by the extra rate: $100 / $10 / point = 10 points. Then add the 10 extra points to the baseline 75 point goal to find the students' average test score: 10 points + 75 points = 85 points. Then added the 8 graded tests to the 2 ungraded tests to find the total number of tests: 2 tests + 8 tests = 10 tests. Then multiply the 85 point average by the number of tests to find the total number of points the students need to earn: 85 points / test * 10 tests = 850 points. Then multiply the current average by the current number of graded tests to find how many points have been earned so far: 70 points / test * 8 tests = 560 points. Then subtract the number of points earned from the number of points needed to find the combine score the last two tests need: 850 points - 560 points = 290 points. The answer is 290.
Question: A farmer owns a hog that recently gave birth to 6 piglets. If the farmer raises the piglets until they are fully grown, he can sell the fully grown pig for $300. Each piglet must grow for at least 12 months before it is large enough to be sold. It costs the farmer $10 per month to feed each animal until it is sold. If the farmer sells 3 pigs after 12 months, and the remaining 3 pigs after 16 months, how much profit did he earn in total (after deducting the cost of food)?
Answer:
The 3 pigs that are sold after 12 months will cost the farmer 12 * 10 * 3 = $360 in food costs. The 3 pigs that are sold after 16 months will cost the farmer 16 * 10 * 3 = $480 in food costs. Thus, the total food cost to raise the 6 piglets was 360 + 480 = $840. Next, selling the 6 fully grown pigs will earn the farmer 6 * 300 = $1800 in revenue. Therefore, the earn the farmer 1800 - 840 = $960 in profit from these sales. The answer is 960.