Solving Linear Word Problems with One Variable A linear word problem is a problem that uses numbers and variables to tell a story or represent a real-wor...
A linear word problem is a problem that uses numbers and variables to tell a story or represent a real-world scenario. These problems involve finding a value of a single variable that satisfies multiple conditions or relationships within the equation.
Let's use the age and fraction puzzles as an example to illustrate how to solve linear word problems with one variable:
Puzzle 1:
John is 5/6 of his father's age. If John's father's age is 42, what is John's age?
Solution:
We can represent this situation mathematically with the equation:
5/6 = x/42
Cross-multiplying, we get:
6(5/6) = 6x
Simplifying the equation:
x = 7
Therefore, John's age is 7.
Puzzle 2:
A farmer has 3/4 of a field devoted to growing corn. If he sells half of his corn, what is the resulting percentage of the field left for corn?
Solution:
First, we convert 3/4 to a decimal:
3/4 = 0.75
Then, we find half of the field by dividing the total area by 2:
0.5 field = 0.5 * 40% = 20%
Therefore, the remaining percentage for corn is 20%.
Additional Notes:
Linear word problems with one variable often involve ratios and proportions.
Finding a single value of the variable that satisfies the equation is the key to solving these problems.
Pay attention to the relationships between the variables in the problem and how they influence each other.
Use the same logic and reasoning to solve linear word problems with different scenarios and variables