Shares

Sharing can be so difficult, especially when it isn't 50:50. Does this question look familiar?


Chris and Pat paint a house. Chris works for 5 hours and Pat works for 3. They are paid $240.00. How much should each get paid?

Of course Pat would say $120.00 but that is not the answer. 

The key to solving is looking at the 2 numbers that AREN'T the total - in this case the 5 and 3. These are the "shares", and they add up to 8. 

If you divide the $240.00 by 8, you will get $30.00. Each share is worth $30.00. Chris worked 5 shares, so will be paid 
$30.00 x 5 - $150.00. 

Pat worked 3 shares, so will be paid $30.00 x 3 - $90.00. 

If you add $150.00 and $90.00, you will get $240.00

Note! Be careful with these types of questions on multiple choice tests. The question might ask, "How much more does Chris earn than Pat?" or something similar. 

Up in the Sky! It's a "Y"

Which is the "x" axis and which is the "y"?

1) Well, "y" is the sky, so it is the vertical axis.

2) A pirate ship is sailing ACROSS the ocean to look for treasure. The captain sees an island on the horizon."X" marks the spot on the treasure map. "X" is the horizontal axis.

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.

Classic "Age" Problems - A couple of ways to solve these questions - Method 1

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

Method 1 - 

a) Create an equation. 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 a letter to represent Pat's age. We'll use "x".

c) If Pat is "x", then Chris has to be 3x.

d) "Together their ages add up to 32..." so...
x + 3x = 32

e) Combine your x's. (That's a lot of alimony). 
4x = 32

f) This means 4 times "something" = 32. The answer is 8. One "x" = 8

g) Pat is 8, because Pat is one "x". Chris is 24 because Chris is 3 times older than Pat.

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