* 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.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*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.

Answer: 7

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?

Answer: 8

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

Answer: 1967

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

Answer: 8

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

Answer: 11

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?

Answer: 15

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

Answer: 45

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: . For example . What is the difference between and ?

Answer: 12

Sept 18: . For example, . How much bigger is than ?

Answer: 7

Sept 19: . For example, . What is ?

Answer: 40

Sept 20: Find the number in the so that the equation holds: .

Answer: 49

Sept 21: What number can go in both boxes so that .

Answer: 5

Sept 22: Find the number in the box. .

Answer: 3

Sept 23: Find one number that can be put in both boxes so that the math equation holds: .

Answer: 35

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.

~~Click GoogleForm to submit answers.~~

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?

Answer: 80 cents

Sept 16: Six apples cost $1.32 and 11 oranges cost as much as 4 apples. What is the cost of 9 oranges?

Answer: 72 cents