Sarah bought 8 folders and 3 rulers. Lea bought 8 rulers and 3 folders. Sarah paid $1.25 more than Lea. How much was each folder if each ruler was 45 cents?
Let the folders cost f.
Let the rulers cost r.
Sarah paid: 8f + 3r
Lea paid: 8r + 3f
Sarah paid 1.25 more than Lea.
8f + 3r = 1.25 + 8r + 3f
5f = 1.25 + 5r
f = 0.25 + r
The rulers cost: r = 0.45
.: f = 0.70
Each folder costs 70 cents.
Check.
8*(0.70) + 3*(0.45) = 6.95
1.25 + 8*0.45) + 3 *(0.70) = 6.95
Okay!
To find the cost of each folder, let's break down the information given in the problem.
Sarah bought 8 folders and 3 rulers, while Lea bought 8 rulers and 3 folders. We know that each ruler costs 45 cents.
If we assume that each folder costs x dollars, we can set up the following equation based on the given information:
8x + 3(0.45) = (8)(0.45) + 3x + 1.25
Here's how we derived this equation:
- The cost of Sarah's folders is 8x since she bought 8 folders.
- The cost of Sarah's rulers is 3(0.45) since each ruler costs 45 cents, and Sarah bought 3 of them.
- The cost of Lea's rulers is (8)(0.45) since she bought 8 rulers.
- The cost of Lea's folders is 3x since she bought 3 folders.
- Sarah paid $1.25 more than Lea, so we add 1.25 to the right side of the equation.
Now, let's solve the equation to find the value of x, which represents the cost of each folder:
8x + 3(0.45) = (8)(0.45) + 3x + 1.25
Simplifying both sides of the equation:
8x + 1.35 = 3.60 + 3x + 1.25
Combining like terms:
8x - 3x = (3.60 + 1.25) - 1.35
5x = 4.50
Dividing both sides of the equation by 5:
x = 0.90
Therefore, each folder costs $0.90.