Class notes Algebra

Here are some examples of algebra word problems, along with a brief explanation of how to set
them up:

1. Age Problem:
- Example: "Anna is 4 years older than her brother. If the sum of their ages is 20, how old are
they?"
- Setup: Let x be the brother's age. Then Anna's age is x + 4. The equation is x + (x + 4) = 20.

2. Distance-Rate-Time Problem:
- Example: "A car travels at a speed of 60 miles per hour. How far does it travel in 3 hours?"
- Setup: Use the formula distance = rate × time. The equation is d = 60 × 3.

3. Mixture Problem:
- Example: "A chemist has a 10% salt solution and a 30% salt solution. How many liters of
each should be mixed to obtain 20 liters of a 20% salt solution?"
- Setup: Let x be the liters of the 10% solution and (20 - x) be the liters of the 30% solution.
Set up the equation based on the total salt content.

4. Work Problem:
- Example: "If it takes 3 hours for 4 workers to complete a task, how long would it take 6
workers to complete the same task?"
- Setup: Use the formula work = rate × time. Set up the equation based on the number of
workers and time.

5. Money Problem:
- Example: "John has $50 more than Mary. Together they have $200. How much does each
have?"
- Setup: Let x be the amount Mary has. Then John has x + 50. The equation is x + (x + 50) =
200.

6. Geometry Problem:
- Example: "The length of a rectangle is twice its width. If the perimeter is 48 meters, what are
the dimensions of the rectangle?"
- Setup: Let w be the width. Then the length is 2w. The equation for the perimeter is 2(w + 2w)
= 48.

7. Consecutive Integers Problem:
- Example: "Find three consecutive integers whose sum is 72."
- Setup: Let x be the first integer. Then the next two integers are x + 1 and x + 2. The equation
is x + (x + 1) + (x + 2) = 72.

8. Percentage Problem:
- Example: "A store is offering a 25% discount on a jacket originally priced at $80. What is the
sale price?"