Sept 2017 (CML)

I will post seven new problems every weekend.  If you like you can try to finish the first 6 problems in 30 minutes, just like in a typical CML test.  The 7th problem is a bonus. 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.

This week we focus on word problems that compute ages, which is also a common theme for CML.

Click GoogleForm to submit answers by Sat, Sept 30.

Week of Sept 24 – 30

Sept 24: Mrs. A is 40 years old and is 4 times as old as her son. Five years ago, she was ___ times as old as her son then.

Sept 25: Tom is 13 and his dad is 48.  How many years ago was his dad 8 times as old as Tom was then?

Sept 26: Michelle will be 16 in 2018.  Her dad was 35 when she was born.  In what year was Michelle’s dad born?

Sept 27: Steve’s age is one quarter his age plus 6.  How old is Steve?

Sept 28: Dad is 29 years older than his son, and their total age is 51.  How old is the son?

Sept 29: Bob’s age is a teenager.   If the two digits in Bob’s age are switched, it becomes Bob’s mom’s age.  Bob’s mom is 36 years older than Bob.  How old is Bob?

Sept 30: Leo, his father and grandfather’s ages form an arithmetic sequence.  Their total age is 135.  How old is Leo’s father?

This week we focus on math equations with “symbols”, which is a common theme for CML.  Sometimes the special symbol represents a math operation; sometimes the symbol represents an unknown number, in which case the problem really is solving an equation with one unknown variable.

Click GoogleForm to submit answers by Sat, Sept 23. Last week’s problems are also due Sept 23.

Week of Sept 17 – 23

Sept 17: $a\Delta b = b+b+a$.  For example $4\Delta 3= 3+3+4=10$. What is the difference between $15\Delta 3$ and $3\Delta 15$?

Sept 18: $a\Delta b = 2a-b$. For example, $4\Delta 3 = 2\times 4-3 = 5$. How much bigger is $12\Delta 1$ than $10\Delta 4$?

Sept 19: $a\Delta b = (a\times b) \div (a-b)$.  For example, $9\Delta 6 = (9\times 6)\div (9-6) = 54\div 3 = 18$. What is $10\Delta 8$?

Sept 20: Find the number in the $\Box$ so that the equation holds: $5 \times 20 = 51+\Box$.

Sept 21: What number can go in both boxes so that $8 - \Box = 2\times \Box - 7$.

Sept 22: Find the number in the box. $27 + 10\times \Box + 15= 72$.

Sept 23:  Find one number that can be put in both boxes so that the math equation holds: $60-\Box = \Box -10$.

This is the first time that I’m putting up CML questions.  The following 7 questions are modeled on the practice problems offered by the Continental Math League for 5th and 6th graders.  Since this is the first week, you have 2 weeks to finish. (Usually you have 1 week.)  Please submit your answers by Saturday, Sept 23.

Week of Sept 10 – 16

Sept 10: Raffle tickets sell for $4 each or 3 tickets for$10. What is the least amount of money one needs to spend to buy 25 tickets?

Answer: $84 Sept 11: If 15 oranges cost$3.30, how much do 25 oranges cost?

Answer: $5.50 Sept 12: Annie has 10 quarters and 5 dimes, and Bonnie has half as many as quarters and twice as many as dimes. How much more money does Annie have than Bonnie? Answer: 75 cents Sept 13: Connie bought a candy bar for 97 cents. The cashier reversed the 2 digits. Connie paid with a 5-dollar bill. How much more change does Connie get back than she should have? Answer: 18 cents Sept 14: Allen bought 8 boxes of crayons at the price of$1.50 per box.  The tax was 5% in addition.  What was the total that Allen paid?

Answer: $12.60 Sept 15: Six apples cost$2.40 and 12 oranges cost as much as 3 apples. What is the cost of 8 oranges?