Example 1 from Algebra and Trigonometry, 2.3 Models and Applications

Modeling a Linear Equation to Solve an Unknown Number Problem

Find a linear equation to solve for the following unknown quantities: One number exceeds another number by $17$ and their sum is $31.$ Find the two numbers.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Let $x$ equal the first number. Then, as the second number exceeds the first by 17, we can write the second number as $x + 17.$ The sum of the two numbers is 31. We usually interpret the word is as an equal sign.

$\begin{matrix} x + (x + 17) & = & 31 \\ 2 x + 17 & = & 31 Simplify and solve . \\ 2 x & = & 14 \\ x & = & 7 \\ x + 17 & = & 7 + 17 \\ = & 24 \end{matrix}$

The two numbers are $7$ and $24.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is $36,$ find the numbers.

How did it go?

Solution

Your turn

Solution

Your turn