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This essential trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 7-8, Math Kangaroo 5-6.

For age problems, observe the following 2 rules:

Time flows for everyone. Jed is three times the age of Ned. Five years from now, Jed will be twice older than Ned. How old is Ned now? equation


equation

equation

equation
J is the age of Jed now and N is the age of Ned now.

Note how the 5 years were added to both J and N.
An age difference does not change in time. Ted is 45 and Zed is 17. How many years ago was Ted 5 times older than Zed? equation

equation

equation

equation
T denotes the age of Ted now. Z denotes the age of Zed now.

Some years ago Zed's age was X and Ted's age was 5X, but the difference was the same: 28 years.

At the time, Zed was 7 - it happened 10 years ago.

For coin problems, remember that the number of coins is different from the monetary value of the coins.

Example of coin problem:

In a piggy bank there are q quarters, d dimes and n nickels. There are twice as many nickels as quarters and half as many quarters as dimes. How many quarters are there if the total amount in the piggy bank is $6.50?

The most important thing is to keep in mind that q, d, and n are numbers of coins, whereas their monetary values are 0.25, 0.1, and 0.05, respectively.

equation

equation

Now compute the monetary value of the coins (in cents):

equation

and set it to equal 650 cents:

equation

equation

There are 10 quarters in the piggy bank.

Examples of time problems:

1 hr = 60 min Every 5/6 of an hour a computer programmer takes 3 minutes to stretch and rest her eyes. All the breaks she takes in an 8 hr workday amount to what total time? equation

equation

equation

equation
Out of every 53 minutes period, 3 minutes are break.
There are 480 min in 8 hours.
9 periods of 53 minutes total 477 minutes.
There are 9 3-minute breaks totaling 27 minutes of break time.
1 min = 60 s The July 22, 2009 solar eclipse lasted 6 minutes and 39 seconds in some places on Earth.
The maximum duration of a solar eclipse has been calculated to be of 7 minutes and 30 seconds.
How much percent of the longest possible duration was the duration of the 2009 eclipse?
equation

equation

equation

equation
Convert the time to seconds in both cases.
The longest possible eclipse lasts 450 seconds. The 2009 eclipse lasted 396 seconds.
Denote the unknown percentage with x.
Solve for x to get 88%.
1hr = 3600 s Hearsay has it that Bill Gates' fortune increases by $150 every second. How much money does he make by sitting around doing nothing for 8 hours a day? equation There is nothing to explain, really.