John spent 1/3 of his money on a pair of shoes and 3/5 of the remainder
on 4 storybooks. He still had $48 left.
(a) How much money did he have at first?
(b) Find the cost of each storybook if each storybook cost the same
amount of money.
x(1 - 1/3 - (3/5)(2/3)) = 48
(a) solve for x
(b) 3/5 * 2/3 = 2/5
so each storybook cost 1/4 * 2/5 x = 1/10 x
money at first ---- x
amount left after getting shoes = 2x/3
amount left after getting books = (2/5)(2x/3)
(2/5)(2x/3) = 48
(4/15)x = 48
x = 180
check: shoes = 1/3 of 180 = 60
leaves him with 120
spends (3/5) of that, or 72, on books
leaves him with 120-72, or 48, as stated.
Surely you can find the cost of each book.
To solve this problem, we need to break it down into smaller steps:
Step 1: Find out how much money John had when he decided to buy the shoes.
To do this, let's assume that John initially had X amount of money. He spent 1/3 of this money on shoes, which means he had 2/3 of X left.
Step 2: Calculate the remaining amount of money after buying the shoes.
To find this amount, we multiply 2/3 of X by (1 - 3/5) to account for him spending 3/5 of the remaining money on storybooks. The resulting amount should be $48.
Step 3: Set up an equation and solve for X.
Now that we have the remaining amount of money, we can set up an equation:
2/3 of X × (1 - 3/5) = $48.
Step 4: Solve the equation to find X.
To solve this equation, we can simplify it:
2/3 of X × 2/5 = $48.
Multiplying the fractions, we get:
4/15 of X = $48.
To isolate X, we can multiply both sides of the equation by the reciprocal of 4/15, which is 15/4:
X = $48 × 15/4.
Step 5: Calculate the value of X.
Now we can calculate the value of X by multiplying $48 by 15 and dividing it by 4:
X = $720.
(a) Therefore, John had $720 initially.
Step 6: Find the cost of each storybook.
Now that we know the initial amount John had, we can find the cost of each storybook. He spent 3/5 of the remaining money on 4 storybooks. To find the cost of each book, we divide the remaining money by the number of storybooks.
Calculating the remaining money:
Remaining money = (2/3 of X) × (1 - 3/5)
= ($720) × (2/3) × (2/5)
= $192.
Dividing the remaining money by the number of storybooks:
Cost of each storybook = Remaining money / Number of storybooks
= $192 / 4
= $48.
(b) Each storybook costs $48.