Unit 1 Problem Solving Challenges

If you feel like you have mastered all of the content covered in Unit 1, give these problem solving challenges a try!  Please email me your response along with a complete mathematical explanation.

“Gran, How Old Are You?”

Mom and her four children live with Grandma at 13 Drywater Street.

One day, Charlie, who is the third child, asked, “Gran, how old are you?”

Grandma answered, “My grandmother would have said ‘As old as my tongue and a little older than my teeth!’ but I will tell you how to work out my age.

“If you multiply your mom’s age with your age and with the ages of your brothers and sisters you will get the answer 111111. If you add your Mom’s age along with the ages of all of you four children the total will be my age.”

Charlie worked this out very quickly, because he knew his Mom’s age, his age and the ages of his brothers and sisters.

“Gran!” he called as he ran off to play outside, “You are old!”  How old was Grandma?

The Moons of Vuvv

The planet of Vuvv has seven moons, which lie spread out on one plane in a great disc round it. These Vuvvian moons all have long and confusing names so scientists usually call them by their initials: A, B, C, D, E, F and G, starting from the nearest one to the planet.

When two of these moons line up with the planet it is called a 'lunar eclipse'. When three line up with the planet it is called a 'double eclipse', when four do it is a 'triple eclipse' and so on. Once in a while all seven moons line up with the planet and this is called a 'super-eclipse'.

Moon A completes a cycle around the planet in one Vuvvian year, Moon B takes 2 years, Moon C takes 3 years, Moon D takes 4 years, and so on.

How long is it between each 'super-eclipse' on the planet of Vuvv?