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
8f+3r = 8r+3f + 1.25
now plug in r=.45 to get
8f+1.35 = 3.60+3f+1.25
5f = 3.50
f = .70
check:
8*.70+3*.45 = 6.95
3*.70+8*.45 = 5.70
difference is 1.25
.70
Let's assume the cost of each folder is $x.
Since Sarah bought 8 folders and 3 rulers, the total cost for Sarah's purchase is:
8x (for the folders) + 3 * $0.45 (for the rulers) = 8x + $1.35
Similarly, since Lea bought 3 folders and 8 rulers, the total cost for Lea's purchase is:
3x (for the folders) + 8 * $0.45 (for the rulers) = 3x + $3.60
According to the problem, Sarah paid $1.25 more than Lea. So we can set up an equation:
8x + $1.35 = 3x + $3.60 + $1.25
Now, let's solve for x:
8x - 3x = $3.60 + $1.25 - $1.35
5x = $3.50
x = $3.50 / 5
x = $0.70
Therefore, each folder costs $0.70.
To find the cost of each folder, we need to determine how much each person paid in total and then divide that total by the number of folders.
Let's start by calculating the total amount paid by Sarah and Lea.
For Sarah, the cost of each ruler is $0.45, and she bought 3 rulers. So the total amount Sarah paid for the rulers is:
3 rulers * $0.45/ruler = $1.35
Now, let's calculate the total amount Sarah paid for the folders. She bought 8 folders, and we need to figure out how much more she paid compared to Lea. We know that Sarah paid $1.25 more than Lea, so by subtracting $1.25 from the total amount Sarah paid, we can find out the cost of the folders:
Total amount Sarah paid - Amount for rulers = Amount for folders
$1.35 - $1.25 = $0.10
So the total amount Sarah paid for the folders is $0.10. To find the cost of each folder, we divide the total amount by the quantity:
Amount for folders / Quantity of folders
$0.10 / 8 folders = $0.0125
Therefore, each folder costs $0.0125, or 1.25 cents.