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Writing Equations Solutions

When writing an equation from a word problem, read the problem carefully. 
Ask yourself, “What are the key pieces of information in this problem?” 
- Circle, highlight, or mark information you think is important. 
- Determine mathematical words being used that imply operations . 
- Sketch a picture if needed. 
Define the variable(s) you will use for the problem.

Example 1

Kelly wrote an article after attending the school art show. The art teacher shared that two-thirds of the submissions were paintings and the rest were pottery. If Kelly counted twenty pieces of pottery, what was the total number of submissions for the art show?

a: art pieces

$\begin{array}{rcl} 1 - \frac{2}{3} & = & \frac{1}{3} of the art is pottery \\ \frac{1}{3} a & = & 20 \\ (3) \frac{1}{3} a & = & 20 (3) \\ a & = & 60 \end{array}$

The art show had 60 art pieces .

Example 2

Daniel bought 4 shirts and a pair of pants. The pants were $25.50. He spent a total of $84.50. How much was each shirt?

x = cost of a shirt

$\begin{array}{rcl} 4 x + 25.50 & = & 84.50 \\ - 25.50 - 25.50 \\ \frac{4 x}{4} & = & \frac{59}{4} \\ x & = & 14.75 \end{array}$

The cost of one shirt is $14.75 .

Example 3

Patrick and Joseph decide to make homemade pasta for dinner. The ratio of cups of flour to eggs is three to two. If nine people are eating dinner, and the recipe notes suggest that you use one egg per person, how much of each ingredient is needed?

f = flour 
e = eggs
p = people

$\frac{p}{e} = \frac{1}{1} \frac{9}{e} = \frac{1}{1} e = 9$

$\begin{matrix} \frac{f}{e} = \frac{3}{2} \\ \begin{array}{rcl} \frac{3}{2} & = & \frac{f}{9} \\ 3 (9) & = & 2 f \\ \frac{27}{2} & = & \frac{2 f}{2} \\ f & = & 13 \frac{1}{2} \end{array} \end{matrix}$

Patrick and Joseph will need $13 \frac{1}{2}$ cups of flour and 9 eggs to make the pasta.