Translating to An Equation and Solving
Translating to An Equation and Solving
In the next few examples, we will translate sentences into equations and then solve the equations. You might want to review the translation table in the previous tutorial.
Example
Translate and solve: The number 143 is the product of \(-11\) and y.
Solution
Begin by translating the sentence into an equation.
| Translate. | |
| Divide by \(-11\). | |
| Simplify. | |
| Check: \(\begin{array}{cccc}& \hfill 143& =& -11y\hfill \\ & \hfill 143& \stackrel{?}{=}& -11\left(-13\right)\hfill \\ & \hfill 143& =& 143✓\hfill \end{array}\) |
Example
Translate and solve: \(n\) divided by 8 is \(-32\).
Solution
| Begin by translating the sentence into an equation.
|
||
| Multiple both sides by 8. | ||
| Simplify. | ||
| Check: | Is \(n\) divided by 8 equal to −32? | |
| Let \(n=-256\). | Is \(-256\) divided by \(8\) equal to \(-32\)? | |
| Translate. | \(\frac{-256}{8}\stackrel{?}{=}-32\) | |
| Simplify. | \(\phantom{\rule{0.6em}{0ex}}-32=-32✓\) | |
Example
Translate and solve: The quotient of \(y\) and \(-4\) is \(68\).
Solution
Begin by translating the sentence into an equation.
| Translate. | ||
| Multiply both sides by \(-4\). | ||
| Simplify. | ||
| Check: | Is the quotient of \(y\) and \(-4\) equal to \(68\)? | |
| Let \(y=-272\). | Is the quotient of \(-272\) and \(-4\) equal to \(68\)? | |
| Translate. | \(\frac{-272}{-4}\stackrel{?}{=}68\) | |
| Simplify. | \(\phantom{\rule{1.3em}{0ex}}68=68✓\) | |
Example
Translate and solve: Three-fourths of \(p\) is 18.
Solution
Begin by translating the sentence into an equation. Remember, “of” translates into multiplication.
| Translate. | ||
| Multiply both sides by \(\frac{4}{3}.\) | ||
| Simplify. | ||
| Check: | Is three-fourths of p equal to 18? | |
| Let \(p=24.\) | Is three-fourths of 24 equal to 18? | |
| Translate. | \(\frac{3}{4}·\phantom{\rule{0.2em}{0ex}}24\phantom{\rule{0.2em}{0ex}}\stackrel{?}{=}18\) | |
| Simplify. | \(\phantom{\rule{1.6em}{0ex}}18=18✓\) | |
Example
Translate and solve: The sum of three-eighths and \(x\) is one-half.
Solution
Begin by translating the sentence into an equation.
| Translate. | |||
| Subtract \(\frac{3}{8}\) from each side. | |||
| Simplify and rewrite fractions with common denominators. | |||
| Simplify. | |||
| Check: | Is the sum of three-eighths and \(x\) equal to one-half? | ||
| \(\text{Let}\phantom{\rule{0.2em}{0ex}}x=\frac{1}{8}.\) | Is the sum of three-eighths and one-eighth equal to one-half? | ||
| Translate. | \(\phantom{\rule{0.2em}{0ex}}\frac{3}{8}+\frac{1}{8}\stackrel{?}{=}\frac{1}{2}\) | ||
| Simplify. | \(\phantom{\rule{2em}{0ex}}\frac{4}{8}\stackrel{?}{=}\frac{1}{2}\) | ||
| Simplify. | \(\phantom{\rule{2em}{0ex}}\frac{1}{2}=\frac{1}{2}✓\) | ||
This lesson is part of:
Solving Linear Equations II