Max has some money. He spends $l,250 on a laptop. He spends 1/5 of the remaining money on a phone. He receives $780 more money. Max now has 3/4 of the amount of money he started with. How much money did Max start with?
If he started with $x, then
(x-1250) * 4/5 + 780 = 3/4 x
Now just solve for x. Post your work if you get stuck.
10202
Let's use the step-by-step approach to solve this problem.
Step 1: Max spent $1,250 on a laptop.
Let's assume the remaining money after buying the laptop is 'x'.
So, Max has x dollars left.
Step 2: Max spends 1/5 of the remaining money on a phone.
The amount Max spent on the phone can be calculated as (1/5) * x = x/5.
After buying the phone, Max has (x - x/5) = (4x/5) dollars left.
Step 3: Max receives $780 more money.
Adding the received money to the remaining amount, Max now has (4x/5) + $780.
Step 4: Max now has 3/4 of the amount of money he started with.
According to the given information, (4x/5) + $780 = (3/4) * x.
Now, let's solve this equation to find the value of x.
(4x/5) + $780 = (3/4) * x
Multiply both sides of the equation by 20 to eliminate fractions:
16x + 15600 = 15x
Subtract 15x from both sides:
16x - 15x + 15600 = 0
x + 15600 = 0
x = 15600
Therefore, Max started with $15,600.
To find out how much money Max started with, let's work through the given information step by step.
1. Max spends $1,250 on a laptop. So, the amount of money remaining is the initial amount minus $1,250.
Initial money - $1,250 = Remaining money
2. Max spends 1/5 of the remaining money on a phone. This means he spends (1/5) * Remaining money on a phone.
Remaining money - (1/5) * Remaining money = Money after buying a phone
3. Max receives $780 more. So, the money after buying a phone plus $780 is equal to 3/4 of the amount of money he started with.
(Money after buying a phone) + $780 = (3/4) * Initial money
Now, we can set up an equation using the given information to solve for the initial amount of money Max had:
(Initial money - $1,250) - (1/5) * (Initial money - $1,250) + $780 = (3/4) * Initial money
To solve this equation, we can follow these steps:
1. Simplify the equation by distributing and combining like terms.
2. Move all terms with Initial money to one side of the equation.
3. Solve for Initial money.
Let's solve the equation step by step:
(Initial money - $1,250) - (1/5) * (Initial money - $1,250) + $780 = (3/4) * Initial money
Multiply through by 20 (the least common multiple of 4 and 5) to eliminate the fractions:
20 * (Initial money - $1,250) - 4 * (Initial money - $1,250) + 20 * $780 = 15 * Initial money
20 * Initial money - 20 * $1,250 - 4 * Initial money + 4 * $1,250 + 20 * $780 = 15 * Initial money
16 * Initial money - 16 * $1,250 + 20 * $780 = 15 * Initial money
Combining like terms:
16 * Initial money - $20,000 + $15,600 = 15 * Initial money
Simplifying:
16 * Initial money - $4,400 = 15 * Initial money
Isolating Initial money:
16 * Initial money - 15 * Initial money = $4,400
Initial money = $4,400
Therefore, Max started with $4,400.