5 Tricky Algebra Word Problems with Simple Step-by-Step Solutions and Charts

1. There and Back Distance = Rate x Time Problems

Ernest Wolfe

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countdown.education

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3 min read

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Nov 1, 2016

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1. Draw a chart

1. Usually, the ‘There’ distance will be the same as the ‘Back’ distance, so you can set these equal to each other in an equation
2. Read the problem to fill in the values they give you and find out what they want you to solve

• “How far” = distance
• “How long” = time
• “How fast” = rate

1. Convert all your values to the same units of distance and time
2. Set up an equation to solve for any missing variables

2. Going Opposite Directions Distance = Rate x Time Problems

1. Draw a chart:

1. Find what value you need to find and set that to x
2. Read the problem to fill in the values the other values they give you

• “How far” = distance
• “How long” = time
• “How fast” = rate

1. Convert all your values to the same units of distance and time
2. Find the combined distance and combined rate by adding up the values of each objet
3. Set up an equation to solve for any missing variables

3. Mixture Problems

1. 1. Draw a chart

1. Find what you want to solve for and set it equal to x
2. If you’re mixing a pure substance, then its concentration is 1.00 (100% solute)
3. If you’re mixing water, then the concentration is 0 (0% solute)
4. To solve for a missing volume, either add or subtract x, using the fact that the volumes of substance 1 and 2 should add up to equal the volume of the complete mixture
5. Set up an equation in the far right column and solve for x
6. Phrase your answer as a complete sentence (“Add 12 mL of 5% solution in order to…”)

4. Investment Problems

1. Draw a table

1. Read the problem to see what you want to solve for and set it to x
2. Plug in values you know for the amounts invested or the amounts gained
3. Set up a formula to solve for variables and missing values
4. Phrase your answer as a complete sentence (“You would invest $1,000 at 5% interest in order to…”)

5. Geometry Problems

1. Know your formulas for area and perimeter of common shapes

• Triangle
• Area = 1/2 base x height
• Perimeter = side 1 + side 2 + side 3
• Rectangle
• Area = base x height
• Perimeter = 2 x base + 2 x height
• Trapezoid
• Area = average base (base 1 + base 2) / 2) x height
• Perimeter = side 1 + side 2 + side 3 + side 4
• Circle
• Area = πr2
• Perimeter (aka circumference) = 2πr or πr

1. Figure out what the problem wants you to solve for, and write an area or perimeter equation to solve it
2. Identify which values and variables the problem provides you with and set up equations for them
3. Make sure your answer makes sense — remember, lengths and areas cannot be negative!
4. Remember units!!