Problem
What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?
A. 2:18:27.6
B. 2:16:00.0
C. 2:17:56.3
D. 2:19:03.1
Coin denominations in the US
| Name | Coin value | Dollar Equivalent |
| Penny | 1 ¢ | \$0.01 |
| Nickel | 5 ¢ | \$0.05 |
| Dime | 10 ¢ | \$0.10 |
| Quarter | 25 ¢ | \$0.25 |
| Half-dollar | 50 ¢ | \$0.50 |
There are 12 dial units in the clock. Every time the minute hand completes 12 dials, the hour hand moves 1 dial. Thus, if the minute hand moves by x the hour hand moves by x/12.
Key equations:
$\dfrac{x}{12}$ = distance traveled by the hour hand (in minutes)
Case 1: Workers have different rates
Work rate = (1 job done) / (Time to finish the job)
Time of doing the job = (1 job done) / (Work rate)
For example
Albert can finish a job in A days
Bryan can finish the same job in B days
Carlo can undo the job in C days
If x = present age of a person
x – 3 = age of the person 3 years ago
x + 5 = age of the person 5 years from now or 5 years hence
Note:
The difference of the ages of two persons is constant at any time.
Motion with constant velocity
The distance traveled is the product of velocity and time.
were,
s = distance
v = velocity
t = time
It follows that
For any three digit number, let
h = the hundreds digit
t = the tens digit and
u = the units digit
The number = 100h + 10t + u
The number with digits reversed = 100u + 10t + h
The sum of digits = h + t + u
The product of digits = htu
There are four common types of mixture in verbal problems of Algebra.
Solutions
Solution is a homogeneous mixture formed by dissolving a substance (solute) in another substance (solvent). A common example is the salt as solute and water as solvent forming into one phase called brine or saline water.
Alloys
An alloy is a solid solution formed by fusing two or more metallic elements. A common alloy is bronze which is the product of fusing iron and copper.
Addition
Expressions that can be translated to addition, ( + ): sum, plus, added to, in addition, increased by, and more than.
| Verbal expression | Algebraic equivalent |
|---|---|
| the sum of x and y | x + y or y + x |
| x plus y | x + y |
| x increased by y | x + y |
| x added to y | y + x |
| x in addition to y | y + x |
| x more than y | y + x |
The following is an attempt to classify the verbal problems.
Number-related problems
Number-related problems are considered as the most basic type of verbal problems. It is taken as the base point of analysis for more complex type of problems.
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