# 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 14 – Oct 20: Word problems with ratios.

Oct 14: The ratio of cats to dogs at the pound is 2:3. If there are 32 cats, how many dogs are there?

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?

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?

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?

Oct 18: For every $3 Mary spends, Andy spends$5. If Andy spends $40 more than Mary, how much money does Mary spend? Oct 19: What is the ratio of 1 pound 4 ounces to 3 pounds 10 ounces? (1 pound = 16 ounces) 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?

Week of Oct 7 – Oct 13: Word problems with fractions.

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?

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 ${2\over 3} - {4\over 5}$?

Week of Sept 30 – Oct 6: All about decimals.

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:
$0.092\times 100$,       $25.5\div 0.5$,      $(0.11)^2$,        $0.025\times 0.4$

Oct 2: Compute the following quantities and express the results in decimals:
$6\over {0.3}$,           $0.3 \over 0.05$,              $2\over 0.4$,        $0.01\over 2$

Oct 3: Express $(0.2)^3 \over {0.02^2}$ as a decimal.

Oct 4: Express ${0.1 \over 2} + {1 \over 0.2}$ as a decimal.

Oct 5: The product of $100\times 3.67 \times 0.367\times 1000$ is the square of what positive number?