Translate to an Equation and Solve

To solve applications algebraically, we will begin by translating from English sentences into equations. Our first step is to look for the word (or words) that would translate to the equals sign. Table 2.1 shows us some of the words that are commonly used.

Equals =
is
is equal to
is the same as
the result is
gives
was
will be

Table 2.1

The steps we use to translate a sentence into an equation are listed below.

How To

Translate an English sentence to an algebraic equation.

Step 1. Locate the "equals" word(s). Translate to an equals sign (=).

Step 2. Translate the words to the left of the "equals" word(s) into an algebraic expression.

Step 3. Translate the words to the right of the "equals" word(s) into an algebraic expression.

Example 2.9

Translate and solve: Eleven more than \(x\) is equal to 54.

Solution
Translate. Eleven more than \(x\) is equal to 54
\(x + 11 = 54\)
Subtract 11 from both sides. \(x+11 -11 = 54-11\)
Simplify. \(x = 43\)
Check: Is 54 eleven more than 43?

\(43 + 11 \stackrel{?}{=} 54\)

\(54 = 54\)✓

Try It 2.17

Translate and solve: Ten more than \(x\) is equal to 41.

Try It 2.18

Translate and solve: Twelve less than \(x\) is equal to 51.

Example 2.10

Translate and solve: The difference of \(12t\) and \(11t\) is −14.

Solution
Translate. The difference of \(12t\) is -14
\(12t - 11t = -14\)
Simplify.  \(t = -14\)
Check:

\(12(-14)-11(-14) =? -14\)

\(-167 + 154 \stackrel{?}{=} -14\)

\(-14 = -14\) ✓

Try It 2.19

Translate and solve: The difference of \(4x\) and \(3x\) is 14.

Try It 2.20

Translate and solve: The difference of \(7a\) and \(6a\) is −8.

Back to '2.2: Addition/Subtraction Property of Equations'