# Bill has 12 hours available to study for his final exams in history and psychology. He decides...

## Question:

Bill has 12 hours available to study for his final exams in history and psychology. He decides that he needs to spend twice as much time studying for history as for psychology. How long should he study?

## Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

For example: 4x +3y = 1 is an algebraic equation where x and y are variables and 1 is the equivalent constant of the relation shown in the equation.

In the word problems of algebraic equation, this relation is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

Let assume that the hours spend on studying psychology is {eq}x, {/eq} then the hours spend on studying history is {eq}2x. {/eq}

According to the question total available time is {eq}12\ hours. {/eq}

$$Total\ time=\ Time_{History} + Time_{Psychology}$$

$$12=\ 2x + x$$

$$12=\ 3x$$

$$4=\ x$$

The hours spend on studying psychology is {eq}4\ hours {/eq} and on history is {eq}8\ hours. {/eq} 