Digit-related Problems

For any three digit number.

x = the hundreds digit
y = the tens digit and
z = the units digit

The number = 100x + 10y + z
The number with digits reversed = 100z + 10y + x
The sum of digits = x + y + z
The product of digits = xyz

In a three digit number, the hundreds digit is twice the units digit. If 396 be subtracted from the number, the order of the digits will be reversed. Find the number if the sum of the digits is 17.

$x$ = hundreds digit
$y$ = tens digit

Mixture-related Problems

There are four common types of mixture in verbal problems of Algebra.

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.

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.

Number-related Problems

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


Right Spherical Triangle

Solution of right spherical triangle
With any two quantities given (three quantities if the right angle is counted), any right spherical triangle can be solved by following the Napier’s rules. The rules are aided with the Napier’s circle. In Napier’s circle, the sides and angle of the triangle are written in consecutive order (not including the right angle), and complimentary angles are taken for quantities opposite the right angle.