A pencil and a ruler cost 2.50 together. The ruler costs $1.00 more than the pencil. How much is the pencil
The Correct Answer and Explanation is:
We are given two pieces of information:
- The total cost of a pencil and a ruler is $2.50.
- The ruler costs $1.00 more than the pencil.
Step 1: Define a variable
Let the cost of the pencil be x dollars.
Then, since the ruler costs $1.00 more than the pencil, the cost of the ruler is x + 1.00 dollars.
Step 2: Set up an equation
The total cost of the pencil and the ruler is $2.50.
So, we can write the equation:
x + (x + 1.00) = 2.50
Step 3: Solve the equation
Combine like terms:
2x + 1.00 = 2.50
Subtract 1.00 from both sides:
2x = 1.50
Divide both sides by 2:
x = 0.75
Final Answer:
The pencil costs $0.75
Explanation
This is a classic example of a word problem involving a system of relationships. The key to solving it is translating the word problem into a mathematical equation using variables.
We begin by letting x represent the unknown price of the pencil. Once we do this, the cost of the ruler must be x + 1.00 because it is given that the ruler costs one dollar more than the pencil.
The total price of both items together is $2.50. By adding the expression for the pencil (x) and the ruler (x + 1.00), we set up an equation that models the situation: x + (x + 1.00) = 2.50. This step is crucial because it captures the relationship described in words in mathematical form.
Combining like terms gives 2x + 1.00 = 2.50, which is a linear equation in one variable. Subtracting 1.00 from both sides isolates the terms with x on one side and the numerical value on the other, giving 2x = 1.50.
Finally, dividing both sides by 2 gives x = 0.75, which is the cost of the pencil.
This solution shows that the pencil costs 75 cents and the ruler, being one dollar more expensive, costs $1.75. Their sum is $0.75 + $1.75 = $2.50, which confirms that the solution is correct.
