Tom had some money. He spent $330 on books and 3/5 of the remainder on toys. After that, he had 1/4 as much money as he had first. How much money did Tom has left?
Let x = amount of money at first
x - 330 - .60(x-330) = .25x
Solve for x, then .25x.
Let's break this problem down step by step:
1. Tom spent $330 on books.
- Remaining money = Total money - money spent on books
2. Tom spent 3/5 of the remainder on toys.
- Money spent on toys = (3/5) * remainder
3. After that, Tom had 1/4 as much money as he had first.
- Remaining money = (1/4) * Total money
Now, let's solve this step by step:
1. Tom spent $330 on books.
Remaining money = Total money - $330
2. Tom spent 3/5 of the remainder on toys.
Money spent on toys = (3/5) * (Total money - $330)
3. After that, Tom had 1/4 as much money as he had first.
Remaining money = (1/4) * Total money
To find the amount of money Tom has left, we need to set up an equation:
Remaining money = Total money - $330 - (3/5) * (Total money - $330) = (1/4) * Total money
Now, let's solve for the remaining money:
(1 - 3/5) * (Total money - $330) = (1/4) * Total money
(2/5) * (Total money - $330) = (1/4) * Total money
Multiplying both sides by 20 to get rid of the fractions:
8 * (Total money - $330) = 5 * Total money
8 * Total money - 8 * $330 = 5 * Total money
8 * Total money - 5 * Total money = 8 * $330
3 * Total money = 8 * $330
Total money = (8 * $330) / 3
Total money ≈ $880
Now, we know the total money Tom had. Let's find the remaining money:
Remaining money = (1/4) * Total money
Remaining money = (1/4) * $880
Remaining money = $220
Therefore, Tom has $220 left.
To find out how much money Tom has left, we need to follow a few steps:
Step 1: Calculate the amount of money Tom had before purchasing books.
Let's assume the amount of money Tom had initially is "x".
Tom spent $330 on books, so the amount of money remaining after this purchase is "x - $330".
Step 2: Calculate the amount Tom spent on toys.
Tom spent 3/5 of the remainder on toys, which is (3/5)*(x - $330).
Step 3: Calculate the amount of money Tom had after purchasing toys.
The amount of money remaining after spending on toys is (x - $330) - (3/5)*(x - $330).
Step 4: Set up the equation based on the given information.
The problem states that after all these purchases, Tom had 1/4 as much money left as he had initially. So, we can set up the equation:
(x - $330) - (3/5)*(x - $330) = (1/4)*x.
Now, let's solve this equation to find the value of x.
(x - $330) - (3/5)*(x - $330) = (1/4)*x
Multiplying the fractions: (5/5)*(x - $330) - (3/5)*(x - $330) = (1/4)*x
Combining like terms: ((5 - 3)/5)*(x - $330) = (1/4)*x
Simplifying: (2/5)*(x - $330) = (1/4)*x
Multiplying both sides of the equation by the common denominators: 8*(2/5)*(x - $330) = 8*(1/4)*x
Simplifying: 16/5*(x - $330) = 2*x
Next, we can distribute the 16/5 on the left side of the equation:
16/5*x - 16/5*$330 = 2*x
To isolate the x terms, we can subtract 16/5*x from both sides:
-16/5*$330 = 2*x - 16/5*x
To further simplify, we can combine the x terms on the right side:
-16/5*$330 = (2 - 16/5)*x
Next, let's simplify the fraction on the right side:
-16/5*$330 = (10/5 - 16/5)*x
To subtract the fractions on the right side, we need a common denominator:
-16/5*$330 = (-6/5)*x
Now, divide both sides by (-6/5) to solve for x:
x = (-16/5*$330)/(-6/5)
Simplifying:
x = $880
Therefore, Tom initially had $880.
Step 5: Calculate the amount of money Tom has left.
Now that we know Tom initially had $880, we can find the amount of money he has left after purchasing books and toys.
Amount spent on books: $330
Amount spent on toys: (3/5)*($880 - $330)
Amount Tom has left: $880 - $330 - (3/5)*($880 - $330)
Calculating the amount left:
Amount Tom has left = $880 - $330 - (3/5)*($880 - $330)
= $880 - $330 - (3/5)*$550
= $880 - $330 - $330
= $880 - $660
= $220
Therefore, Tom has $220 left after all the purchases.