Annika borrowed a book from the library and forgot to return it on time. The library charges $0.25 per day for the first four days and $0.30 per day for all of the remaining days. If Annika had to pay the library $4.00, how many days late was her book?
4-1 = $3 for all the days after day 4. That is ten more days so 14 days total
For 4 days price is 4 ∙ $0.25 = $1
number of days = d
For the total charge after 4 days would be $1 + $0.3 ( d - 4 )
That's because the number of days after the fourth day is d - 4
Set this expression equal to $4 and solve for d:
1+ 0.3 ( d - 4 ) = 4
1 + 0.3 d - 1.2 = 4
0.3 d - 0.2 = 4
Add 0.2 to both sides:
0.3 d = 4.2
Divide both sides by 0.3
d = 4.2 / 0.3 = 14
If you were doing this problem, how would you explain it?
To find out how many days late Annika's book was, we need to calculate the total late fee she had to pay, given the given charges per day.
Let's break down the calculation step by step:
First, we need to figure out the late fee for the first four days, which is charged at a rate of $0.25 per day. We'll represent this as x:
x = 0.25 * number of days within the first four days
Next, we need to determine the late fee for the remaining days after the initial four days. This is charged at a rate of $0.30 per day. We'll represent this as y:
y = 0.30 * number of remaining days
Now, we can calculate the total late fee by adding x and y together:
Total late fee = x + y
We also know from the problem that the total late fee is $4.00.
So, we can form an equation:
0.25 * number of days within the first four days + 0.30 * number of remaining days = 4.00
To solve this equation, we need to find the values of "number of days within the first four days" and "number of remaining days".
Let's assume "number of days within the first four days" is denoted by d1, and "number of remaining days" is denoted by d2.
Therefore, the equation becomes:
0.25 * d1 + 0.30 * d2 = 4.00
Now we need to rearrange the equation to solve for one of the variables. Let's solve for d2:
0.30 * d2 = 4.00 - 0.25 * d1
d2 = (4.00 - 0.25 * d1)/0.30
We can start by assuming a value for d1, for example, let's assume d1 is 10 (it could be any value based on the given information). Plugging this into the equation, we can find d2:
d2 = (4.00 - 0.25 * 10)/0.30
d2 = (4.00 - 2.50)/0.30
d2 = 1.50/0.30
d2 = 5
If we assume d1 as 10, then d2 turns out to be 5. This means Annika was late by a total of 10 + 5 = 15 days.
However, to find the precise number of days, you'll need to solve the equation for d1 and d2 simultaneously. You can use methods such as substitution or elimination to solve the equation.