[Question]An archaeologist discovered three dig sites from different periods in one area. The archaeologist dated the first dig site as 352 years more recent than the second dig site. The third dig site was dated 3700 years older than the first dig site. The fourth dig site was twice as old as the third dig site. The archaeologist studied the fourth dig site’s relics and gave the site a date of 8400 BC. What year did the archaeologist date the second dig site?
[Answer]The third dig site was dated from the year 8400 / 2 = 4200 BC. Thus, the first dig site was dated from the year 4200 - 3700 = 500 BC. The second dig site was 352 years older, so it was dated from the year 500 + 352 = 852 BC. The answer is 852.
Q: Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?
A: Wilson had $150 + $17 = $167 two months ago before making a withdrawal. His money in his account now is $150 + $16 = $166. Since he deposited $21 this month, this means there was $166 - $21 = $145 last month after making a withdrawal. Therefore, Wilson withdrew $167 - $145 = $22. The answer is 22.
Question: Tom and Devin have been teaching for a total of 70 years. Devin has been teaching for 5 less than half the number of years that Tom has. How many years has Tom been teaching?
Answer: Let x be the number of years Tom has been teaching. Devin has been teaching for (1 / 2)x - 5 years. 70 = x + ((1 / 2)x - 5). 70 = (3 / 2)x - 5. 75 = (3 / 2)x. x = 50. Tom has been teaching for 50 years. The answer is 50.
[Question]It takes John 13 seconds to run 100 meters. He only goes 4 meters in the first second. He then maintains the same speed for the rest of the race. James is 2 m/s faster at the top speed and he can run the first 10 meters in 2 seconds. How long does it take James to run 100 meters?
[Answer]John runs 100 - 4 = 96 meters once he reaches his max speed. He runs it in 13 - 1 = 12 seconds. So he runs at a speed of 96 / 12 = 8 m / s. So that means James's top speed is 8 + 2 = 10 m / s. He has to run 100 - 10 = 90 meters at his top speed. So he runs that at 90 / 10 = 9 seconds. So he takes 9 + 2 = 11 seconds to run 100 meters. The answer is 11.
Q: Clive is buying olives for dinner. He has $10 to spend and needs 80 olives. A jar of 20 olives costs $1.50. How much change will Clive have when he buys what he needs?
A: He needs 4 jars of olives because 80 / 20 = 4. He will spend $6 because 4 x 1.5 = 6. He will have $4 in change because 10 - 6 = 4. The answer is 4.
Question: Kenneth has $50 to go to the store. Kenneth bought 2 baguettes and 2 bottles of water. Each baguette cost $2 and each bottle of water cost $1. How much money does Kenneth have left?
Answer:
The cost of the baguettes is 2 × $2 = $4. The cost of the water is 2 × $1 = $2. The total cost of the shopping is $4 + $2 = $6. Kenneth has $50 − $6 = $44 left. The answer is 44.