Edmund bought 3 assessment books. The average cost of the 3 books was $9.80. The Science book cost $0.70 more than the Mathematics book.
The English book cost $0.85 less than the Mathematics book.
Find the total cost of the cheapest book and the most expensive book
Let the cost of the Mathematics book be x.
The cost of the Science book is x + 0.70.
The cost of the English book is x - 0.85.
The average cost of the three books is (x + x + 0.70 + x - 0.85)/3 = $9.80.
Combining like terms, we get (3x - 0.15)/3 = $9.80.
Multiplying both sides of the equation by 3 gives us 3x - 0.15 = $29.40.
Adding 0.15 to both sides gives us 3x = $29.55.
Dividing both sides by 3 gives us x = $9.85.
So, the cost of the Mathematics book is $9.85.
The cost of the Science book is $9.85 + $0.70 = $10.55.
The cost of the English book is $9.85 - $0.85 = $9.00.
Therefore, the total cost of the cheapest book is $9.00 and the most expensive book is $10.55.
To solve this problem, we can use algebraic equations to represent the given information. Let's define the cost of the Mathematics book as "x" dollars.
According to the problem, the Science book cost $0.70 more than the Mathematics book, so its cost can be represented as "x + 0.70" dollars.
Similarly, the English book cost $0.85 less than the Mathematics book, so its cost can be represented as "x - 0.85" dollars.
Now, we can find the average cost of the 3 books by adding the costs of the three books and dividing by 3:
(x + x + 0.70 + x - 0.85) / 3 = 9.80
Combining like terms, we have:
(3x - 0.15) / 3 = 9.80
Multiplying both sides of the equation by 3 to eliminate the fraction:
3x - 0.15 = 29.40
Adding 0.15 to both sides of the equation:
3x = 29.55
Dividing both sides of the equation by 3:
x = 9.85
Therefore, we have found that the cost of the Mathematics book is $9.85.
To find the cost of the Science book, we substitute the value of x into its representation:
Cost of Science book = x + 0.70 = 9.85 + 0.70 = $10.55
To find the cost of the English book, we substitute the value of x into its representation:
Cost of English book = x - 0.85 = 9.85 - 0.85 = $9.00
So, the total cost of the cheapest book (English) is $9.00, and the total cost of the most expensive book (Science) is $10.55.
Let's denote the cost of the Mathematics book as X dollars.
Since the Science book cost $0.70 more than the Mathematics book, the cost of the Science book would be X + $0.70.
Similarly, the English book cost $0.85 less than the Mathematics book, so the cost of the English book would be X - $0.85.
Given that the average cost of the 3 books is $9.80, we can set up the following equation:
(X + (X + $0.70) + (X - $0.85))/3 = $9.80
Multiplying both sides of the equation by 3 to eliminate the fraction, we get:
3X + (X + $0.70) + (X - $0.85) = $29.40
Simplifying the equation, we have:
5X - $0.15 = $29.40
Adding $0.15 to both sides, we have:
5X = $29.55
Dividing both sides by 5, we get:
X = $5.91
Now we can find the cost of each book:
The cost of the Mathematics book is $5.91.
The cost of the Science book is $5.91 + $0.70 = $6.61.
The cost of the English book is $5.91 - $0.85 = $5.06.
To find the total cost of the cheapest book and the most expensive book, we add the costs of the three books:
Total cost of the cheapest book = $5.06
Total cost of the most expensive book = $6.61