Serena paid $20.20 for 36 rulers and folders. She bought 16 more folders than rulers. If each folder cost $0.50 more than each ruler, how much did each folder cost?
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Serene paid $20.20 for 36 items of rules and files.there were 16 more files than rulers.if each file cost $.50 more than each ruler,how much did each file cost?
Let's start by calculating the number of rulers Serena bought. We know that she bought 36 rulers and folders altogether. Since she bought 16 more folders than rulers, we can subtract 16 from the total: 36 - 16 = 20 rulers.
Next, we need to find out how much Serena paid for all the rulers. We know that she paid a total of $20.20, so we divide that by the number of rulers she bought: $20.20 / 20 rulers = $1.01 per ruler.
Now we can figure out the cost of each folder. We know that each folder cost $0.50 more than each ruler, so we add $0.50 to the cost of each ruler: $1.01 + $0.50 = $1.51 per folder.
Therefore, each folder cost $1.51.
To solve this problem, we can set up a system of equations using the given information.
Let's assume x represents the cost of each ruler in dollars.
Since each folder cost $0.50 more than each ruler, the cost of each folder can be represented as x + $0.50.
The total number of rulers and folders purchased is 36.
We know that Serena bought 16 more folders than rulers, so the number of rulers is x and the number of folders is x + 16.
The total amount Serena paid is $20.20.
We can set up the equation:
(x * number of rulers) + (cost of each ruler) + (x + 16) * (cost of each folder) = $20.20
Substituting the values and rearranging the equation, we get:
(x * x) + (x * $0.50) + (x + 16) * (x + $0.50) = $20.20
Simplifying the equation, we have:
x^2 + 0.50x + (x^2 + 0.50x + 16x + $8) = $20.20
Combining like terms, we get:
2x^2 + 17x + $8 = $20.20
Rearranging the equation, we have:
2x^2 + 17x + $8 - $20.20 = 0
Simplifying further, we get:
2x^2 + 17x - $12.20 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-(17) ± √(17^2 - 4(2)(-12.20))) / (2(2))
Simplifying further, we have:
x = (-17 ± √(289 + 97.60)) / 4
Simplifying the square root, we get:
x = (-17 ± √386.60) / 4
Taking the square root of 386.60, we have:
x = (-17 ± 19.66) / 4
Now, we can calculate the two possible values for x:
1. x = (-17 + 19.66) / 4 = 2.66 / 4 = 0.665
2. x = (-17 - 19.66) / 4 = -36.66 / 4 = -9.165
Since the cost cannot be negative, we can discard the second value.
Therefore, the cost of each ruler is approximately $0.665.
To find the cost of each folder, we can add $0.50 to the cost of each ruler:
Cost of each folder = Cost of each ruler + $0.50 = $0.665 + $0.50 = $1.165
Therefore, each folder costs approximately $1.165.