A ballpoint pen cost 8 times as much as an exercise book. John spent 2/5 of his money one exercise books and 1/3 of the remainder on 3 ballpoint pens. How many exercise books did he buy?
1/3 (1 - 2/5) = 1/5 spent on 3 books
so each book cost 1/15 of his money
each pen cost 8/15 of his money
he could only buy one exercise book.
If your question means:
John spent 2 / 5 of his money on exercise books, not for one exercise book
then:
m = John´s money
b = price of ballpoint pen
e = price of an exercise book
b = 8 e
When John spent 2 m / 5 on exercise books remainder = m - 2 m / 5 = 5 m / 5 - 2 m / 5 = 3 m / 5
1 / 3 of the remainder = ( 1 / 3 ) ∙ 3 m / 5 = m / 5
1 / 3 of the remainder = 3 ballpoint pens
m / 5 = 3 b
Multiply both sides by 5
m = 15 b
m = 15 ∙ 8 e
m = 120 e
For his money he can buy 120 exercise books.
John spent 2 / 5 of his money on exercise books means:
2 m / 5 = 2 / 5 ∙120 e = 240 e / 5 = 48 e
He buy 48 exercise books.
my bad - I got lost in the details.
Thanks for watching.
To solve this problem, let's break it down step by step.
Step 1: Assign variables
Let's assign variables to the unknowns in the problem.
Let's say the cost of an exercise book is "x" (in some currency).
Since the ballpoint pen costs 8 times as much as the exercise book, the cost of a ballpoint pen would be 8x.
Step 2: Calculate John's expenses on exercise books
John spent 2/5 of his money on exercise books. This means he spent 2/5 * Total money he had.
Let's represent the total amount of money John had as "initial_money."
Therefore, John spent 2/5 * initial_money on exercise books.
Step 3: Calculate the remainder of John's money after buying exercise books
The remainder of John's money after buying exercise books is (initial_money - 2/5 * initial_money).
This simplifies to (3/5 * initial_money).
Step 4: Calculate John's expenses on ballpoint pens
John spent 1/3 of the remainder of his money on 3 ballpoint pens. This means he spent 1/3 * (3/5 * initial_money) on ballpoint pens.
Since the cost of a ballpoint pen is 8 times the cost of an exercise book, John spent 8x * 3 on ballpoint pens.
Step 5: Set up an equation to solve for x
By adding John's expenses on exercise books and ballpoint pens, we can set up an equation to solve for x:
2/5 * initial_money + 1/3 * (3/5 * initial_money) = 8x * 3.
Step 6: Solve the equation for x
Simplify the left side of the equation:
2/5 * initial_money + 1/3 * (3/5 * initial_money) = (2/5 + 1/3 * 3/5) * initial_money.
Simplifying further:
2/5 * initial_money + 1/3 * (3/5 * initial_money) = (2/5 + 3/5) * initial_money.
Combining like terms:
2/5 * initial_money + 1/3 * (3/5 * initial_money) = 1 * initial_money.
This means that 8x * 3 = initial_money, so 24x = initial_money.
Step 7: Calculate the value of x
Since we know that 24x = initial_money, we can solve for the value of x by dividing both sides of the equation by 24:
x = initial_money / 24.
Step 8: Calculate the number of exercise books John bought
Since the cost of an exercise book is x, we can substitute the value of x into the equation to find out how many exercise books John bought.
Number of exercise books = (2/5 * initial_money) / x.
Plugging in the values, we get:
Number of exercise books = (2/5 * initial_money) / (initial_money / 24).
Simplifying further:
Number of exercise books = (2/5 * 24).
Therefore, John bought (2/5 * 24) exercise books.