Translate the problem into two linear equations by identifying keywords that represent a mathematical operation or symbol.
To translate a problem into two linear equations, you need to identify keywords that represent mathematical operations or symbols. Here are some keywords and phrases commonly used in problems that can help you identify the mathematical operations:
1. Addition and Subtraction:
- "Sum of," "total," "more than," "increased by" (represent addition).
- "Difference between," "less than," "decreased by" (represent subtraction).
2. Multiplication and Division:
- "Product of," "multiplied by," "times" (represent multiplication).
- "Quotient of," "divided by," "per" (represent division).
3. Equality:
- "Is," "equals," "yields," "gives" (represent equality).
Once you have identified these keywords, you can use them to form equations. Let's look at an example problem and identify the keywords:
Example problem: "The sum of two numbers is 10. The difference between the two numbers is 4."
Keywords:
- "Sum" indicates addition.
- "Difference" indicates subtraction.
Using these keywords, we can create two linear equations:
1. The sum of two numbers is 10:
- Let's say the two numbers are x and y. The equation would be: x + y = 10.
2. The difference between the two numbers is 4:
- The order matters here, so we'll subtract the smaller number from the larger one:
- If x > y, the equation would be: x - y = 4.
- If y > x, the equation would be: y - x = 4.
By identifying the keywords and understanding the operations they represent, you can translate a problem into linear equations.