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.

Question: Jeff bought 6 pairs of shoes and 4 jerseys for $560. Jerseys cost 1/4 price of one pair of shoes. Find the shoe's price total price.
Answer: Let X be the shoe price. The jersey's price is 1 / 4 * X. Jeff bought 6 pairs of shoes and 4 jerseys for 6 * X + 4 * (1 / 4X) = $560. Multiplying through the parentheses produces 6X + X = $560. Combining like terms produces 7X = $560. Dividing both sides by 7 produces X = $80, so the shoe price is $80. Since Jeff bought 6 pairs of shoes, he spent 80 * 6 = $480 on shoes. The answer is 480.

Question: Mary is writing a story, and wants her 60 characters to be split according to their initials. Half of her characters have the initial A, and half of this amount have the initial C. Mary wants the rest of her characters to have the initials D and E, but she wants there to be twice as many characters with the initial D as there are characters with the initial E. How many of Mary’s characters have the initial D?
Answer: Half the characters have the initial A, which is a total of 60 / 2 = 30 characters. This means that 30 / 2 = 15 characters have the initial C. Mary wants the remaining 60 – 30 – 15 = 15 characters to have the initials D or E. For there to be twice as many characters with the initial D, the characters are divided into 2 + 1 = 3 parts. Dividing by this means there are 15 / 3 = 5 characters with the initial E. This leaves 15 – 5 = 10 characters with the initial D. The answer is 10.

Question: Hansel makes $30,000 a year and just received a 10% raise. Gretel makes the same amount as Hansel but received a 15% raise. How much more money will Gretel make compared to Hansel?
Answer:
Hansel makes $30,000 and received a 10% raise so his raise is 30,000 * .10 = $3,000.00. Hansel now makes 30,000 + 3,000 = $33,000 a year. Gretel makes $30,000 and received a 15% raise so her raise is 30,000 * .15 = $4,500.00. Gretel now makes 30,000 + 4,500 = $34,500 a year. If Gretel makes $34,500 a year and Hansel makes $33,000 then Gretel makes 34,500 - 33,000 = $1,500 more a year than Hansel. The answer is 1500.