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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?
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Find the product and explain the process and reasoning.
$0.79 x 3.7
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Use the order of operations to find the value of the expression.
5x2+6-5
To find the answer to the first question, "how many days late was Annika's book," we can set up an equation based on the information given:
Let's assume the number of days Annika was late is represented by "x."
From the problem, we know that the library charges $0.25 per day for the first four days. So, for these four days, Annika would be charged $0.25 multiplied by 4, which is $1.00.
The remaining days would be x - 4 days, and the library charges $0.30 per day for these days. Thus, the charge for the remaining days is $0.30 multiplied by (x - 4), which is 0.30x - 1.20.
Since Annika had to pay the library $4.00 in total, we can set up the equation:
1.00 + 0.30x - 1.20 = 4.00
Combining like terms, we get:
0.30x - 0.20 = 4.00
Subtracting 0.20 from both sides, we have:
0.30x = 4.20
Dividing both sides by 0.30, we find:
x = 14
Therefore, Annika's book was 14 days late.
To find the answer to the second question, we need to find the product of $0.79 and 3.7:
Multiply the decimal numbers as you would with whole numbers, ignoring the decimal points:
79 x 37 = 2923
Now, count the number of decimal places in the original numbers (0.79 has 2 decimal places, and 3.7 has 1 decimal place):
Add up the total number of decimal places (2 + 1 = 3).
Place the decimal point in the result by moving from the rightmost digit of the product three places to the left. In this case, the decimal point should be placed after the digit 2, resulting in 2.923.
Therefore, the product of $0.79 and 3.7 is $2.923.
To solve the third question and find the value of the expression 5x2+6-5 using the order of operations (also known as PEMDAS):
The order of operations states that we should first perform any calculations within parentheses, then evaluate exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).
In this expression, there are no parentheses or exponents.
Now, let's evaluate the multiplication and division operations:
5 multiplied by 2 equals 10.
Next, we perform the addition and subtraction:
10 + 6 - 5 equals 11.
Therefore, the value of the expression 5x2+6-5 is 11.