# Oct 2018 (CML)

I will post seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

For instructions on submitting weekly answers, click on the “Logistics” tab.
For previously posted problems, click on the “Archive” tab.
For previous prizes, click on the “News” tab.

Week of Oct 28 – Nov 3: More word problems on ratios.

Oct 28: Compute 40% of 20% of 10% of 80000.

Oct 29: 40% of 20% of 10% of what number is 10?

Oct 30: 18% of 50 is what percent of 24?

Oct 31: 18% of what number is 40% of 45?

Nov 1: A shopper paid $100 for a coat that was on sale for 20% off. How much was the original price of the coat? Answer:$125

Nov 2: The sales tax is 8%. If Jenny paid $216 in total (including tax) for a winter jacket, how much was the jacket before tax? Answer:$200

Nov 3: At the beginning of each month, Mary’s clothing shop marks down an item by 10% of the ticket price if the item wasn’t sold during the past month. A hat was marked $50 at the beginning of Feb. If it wasn’t sold, how much was the hat at the beginning of April? Round your number to the nearest integer. Answer: 50*90%*90%=$40.5~$41 Week of Oct 21 – Oct 27: More word problems on ratios. Click GoogleForm to submit answers by Sat, Oct 27. Oct 21: The statue of Abraham Lincoln in the Lincoln Memorial in DC is 6 meters tall. On the back of the$5 bill, the statue is 5 centimeters tall. If the Memorial measures 25cm tall on the back of the $5 bill, and assuming the bill is drawn to scale, then how tall is the actual Memorial in DC? Answer: $25\div 5 \times 6 = 30$ meters. Oct 22: Two mountains are $5{7\over 8}$ inches apart. If $1\over 2$ of an inch on the map represents 60 miles, how many miles apart are the two mountains? Answer: ${47\over 8} \times 120 = 705$ miles. Oct 23: A fortnight is 14 days, and a mile is 8 furlongs. If a desert caravan travels 12 miles per day, then how many furlongs does it travel in a fortnight? Answer: $12\times 14 \times 8 = 1344$ miles. Oct 24: A 3-inch by 5-inch photo is enlarged proportionally so that the small dimension is 1 foot. What is the area of the enlarged photo in square inches? Answer: $12 \times 20 = 240$ square inches. Oct 25: On a Canada map, the distance between the dots representing Montreal and Quebec City is 10cm. If the scale of the map is ${4\over 9} mm = 1km$, then how far apart are Montreal and Quebec City? Answer: $100 \div {4\over 9} = 225$km. Oct 26: Lily’s 12-foot by 15-foot bedroom is drawn to 4 inches by 5 inches on the construction map. What is the scale of the map? Answer: 1in = 3 ft Oct 27: Mike’s 45 dimes are divided into 3 piles in the ratio of 2:1:6. How many dimes are there in the pile with the least number of dimes? Answer: 5 Week of Oct 14 – Oct 20: Word problems on ratios. Click GoogleForm to submit answers by Sat, Oct 20. Oct 14: The ratio of cats to dogs at the pound is 2:3. If there are 32 cats, how many dogs are there? Answer: $32\div 2\times 3 = 48$. Oct 15: The ratio of boys to girls in a class is 4:5. If the total number of students in the class is 72, how many boys are there? Answer: $72\div (4+5)\times 4 = 32$ Oct 16: A board that is 12 inches long is cut into 2 pieces whose lengths have a ratio of 1:5. What is the length of the longer piece? Answer: $12\div (1+5)\times 5 = 10$ Oct 17: The ratio of teachers to students in a school is 2 to 17. How many teachers are present if there are 85 students? Answer: $85\div 17\times 2 = 10$ Oct 18: For every$3 Mary spends, Andy spends $5. If Andy spends$40 more than Mary, how much money does Mary spend?

Answer: $40\div 2 \times 3= 60$

Oct 19: What is the ratio of 1 pound 4 ounces to 3 pounds 10 ounces? (1 pound = 16 ounces)

Answer: 20: 58 = 10: 29

Oct 20: Four partners in a business split the profit in the ratio 2:3:3:5. If the profit one year is $26000, what is the largest amount of profit received by the one of the four partners? Answer: $26000\div (2+3+3+5) \times 5 = 10000$ Week of Oct 7 – Oct 13: Word problems on fractions. Click GoogleForm to submit answers by Sat, Oct 13. Oct 7: Mary begins with her work at 8:20am and estimates that it’ll take her $5{7\over 10}$ hours to finish. At what time does she expect to finish? Answer: 14:02pm Oct 8: Kevin pays $1\over 3$ of his income in tax. He spends $4 \over 5$ of what remains after tax, and places the rest into his bank account. What fraction of his income does he put into his bank account? Answer: $1-{1\over 3}- {2\over 3}\cdot {4\over 5} = {2\over 15}$ Oct 9: Sam bought $3 {1\over 4}$ pounds of cheese. He used half of the cheese for a casserole and $1\over 4$ pounds for sandwiches. Express as a mixed number the amount of cheese he has left. Answer: ${13\over 4}\cdot {1\over 2} -{1\over 4} = {11\over 8} = 1{3\over 8}$. Oct 10: Matthew starts with 400 pennies. He gives $3\over 5$ of his pennies to his brother and gives $3\over 4$ of his remaining pennies to his sister. How many more pennies does Matthew give to his brother than to his sister? Answer: $400\cdot ( {3\over 5} - {2\over 5}\cdot {3\over 4}) = 400\cdot {3\over 10} = 120$ Oct 11: If $12{2\over 3}$ feet of steel tubing are needed to make one stool, how many feet of tubing are needed to make 300 stools? Answer: $12{2\over 3} \cdot 300 = 3800$ Oct 12: The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number? Answer: ${1\over {1/5 + 1/7}} = {35\over 12}$ Oct 13: Which whole number is closest to ${2\over 3} - {4\over 5}$? Answer: 0 Week of Sept 30 – Oct 6: All about decimals. Click GoogleForm to submit answers by Sat, Oct 6. Sept 30: Arrange the following numbers from smallest to largest: 0.97, 0.979, 0.9709, 0.907, 0.9089 Answer: 0.907, 0.9089, 0.97, 0.9709, 0.979 Oct 1: Compute the following quantities and express the results in decimals: $0.092\times 100$, $25.5\div 0.5$, $(0.11)^2$, $0.025\times 0.4$ Answer: 9.2, 51, 0.0121, 0.01 Oct 2: Compute the following quantities and express the results in decimals: $6\over {0.3}$, $0.3 \over 0.05$, $2\over 0.4$, $0.01\over 2$ Answer: 20, 6, 5, 0.005 Oct 3: Express $(0.2)^3 \over {0.02^2}$ as a decimal. Answer: 20 Oct 4: Express ${0.1 \over 2} + {1 \over 0.2}$ as a decimal. Answer: 5.05 Oct 5: The product of $100\times 3.67 \times 0.367\times 1000$ is the square of what positive number? Answer: 367 Oct 6: If it costs 2.5 cents to copy a page, how many pages can you copy with$10?