Translation

Translation are the most basic types of word problems appearing on the Calculator Applications test. You simply translate the words into their mathematical equivalents and solve.

Here is a table of terms to know for these problems:

Term Definition
sum result of addition
difference result of subtraction
product result of multiplication
quotient result of division
is equals
of multiply (sometimes); apply function to
per divide
absolute positive value
remainder left over part
Example
Compute the square root of the sum of pi and one-half of 7.88.
Solution

Translating the words of the problem into mathematical equivalents, start with "one-half of 7.88". This is the same as $0.5 \times 7.88$, since one-half is 0.5 and "of" represents multiplication here. Next, "sum of" means to add the two parts, so we get $\pi + 0.5 \times 7.88$. Finally, "square root of" means to take the square root of the previous sum: $\sqrt{\pi + 0.5 \times 7.88} = 2.66$.

Be sure and watch the order of operations here.

Remainders

When $A$ is divided by $B$ (where $B$ is positive), the remainder is the part left over after removing a whole number multiple of $B$'s from $A$.

In an equation, this is $A = nB + R$, where $n$ is a whole number and $R$ is the remainder, with $0 \leq R < B$.

You are undoubtably used to finding remainders with whole numbers, like "What is the remainder when 37 is divided by 5?" ($37 = 7\times 5 + 2$ gives a remainder of 2), but we can do it with decimal values as well.

Example
What is the remainder when 48.9 is divided by 6.5?
Solution

First, divide 48.9 by 6.5. $48.9 \div 6.5$ gives $7.523$. Remove the whole number part of this quotient and use the decimal only. This gives us $0.523$. This is NOT the remainder; rather, it is the portion of the divisor that is left over. Inflate this back to the remainder by multiplying by the divisor: $0.523 \times 6.5 = 3.40$.

Age Problems
The key to age problems is to remember to add or subtract years when working with a person's age in their future or past.
Example
Betty is 6 years older than Theresa. Twelve years ago, Betty was twice as old as Theresa. How old will Betty be in three years?
(integer)
Solution

Let $B$ be Betty's age and $T$ be Theresa's age. The first sentence gives the equation $B = T + 6$.

Twelve years ago, Betty's age was $B - 12$ and Theresa's age was $T - 12$. Back then, Betty was twice as old as Theresa: $B - 12 = 2(T - 12)$. [Notice, this is NOT $B = 2T$ because $B$ and $T$ represent their present ages.]

Since we are ultimately looking for Betty's age three years from now, we need to solve for $T$ first. Then, we will substitute this expression into the second equation to solve for $B$.

Solving the first equation for $T$ we get $T = B - 6$.

Substitute into the second equation:

$$\begin{aligned} B - 12 &= 2(B - 6 - 12) \\ B - 12 &= 2(B - 18) \\ B - 12 &= 2B - 36 \\ B &= 24 \end{aligned}$$

Three years from now, $B + 3$, Betty will be 27 years old.