Age Problems - Method 2 - Substitution

Chris is 3 times as old as Pat.               Together their ages add up to 32.                          How old is each of them?

Method 2 - "Game Show" Higher or Lower Method

a) Pat is your "reference" or starting point. Look for the word "as" or "than". (The first sentence could have been written "Chris is 3 times older than Pat.") The word associated with "as" or "than" becomes your reference. 

b) Pick 1 to represent Pat's age. 

c) If Pat is 1, then Chris has to be 3 because "Chris is 3 times as old as Pat."

d) "Together their ages add up to 32..." so...
1 + 3 will not work, as it doesn't = 32. The answer is too low. Pick a higher number to represent Pat's age. 

e) Pick 10 to represent Pat's age. 

f) If Pat is 10, then Chris has to be 30 because "Chris is 3 times as old as Pat."

g) "Together their ages add up to 32..." so...

10 + 30 will not work, as it doesn't = 32. The answer is too high. Pick a lower number to represent Pat's age. 


h) Eventually, by going higher and lower, you'll figure out that Pat is 8. Chris is 24 because Chris is 3 times older than Pat.

i) Check! Always check! "Together their ages add up to 32."       8 + 24 = 32.