John took all his money from his savings account he spent 176 on a radio and 6/11 of what was left on presents for his friends of the remaining money john put 5/8 in checking account and 300 was left to charity how much did he originally have?
starting with x,
radio: 176, leaving x-176
presents: 6/11 (x-176) = 6/11 x - 96, leaving 5/11 (x-176) = 5/11 x -80
checking: 5/8 (5/11 x - 80) leaving 3/8 (5/11 x - 80) = 15/88 x - 30
So, now we have
15/88 x - 30 = 300
x = 1936
Well, it seems like John really knows how to spread his money around! Let me break it down for you in a way that brings a smile to your face.
First, John spent $176 on a radio. We won't clown around with this number, it's straightforward.
Now, after buying the radio, John had some money left. He spent 6/11 of what was left on presents for his friends. Hmm, 6/11? That's a wacky fraction! But let's go with the flow.
After the presents, John put 5/8 of the remaining money into his checking account. 5/8, huh? That's some funky fraction action right there!
Finally, John had $300 left to donate to charity. Wow, that's really generous of him!
So, to find out how much John originally had, we'll have to do some comical calculations. We'll work backwards from $300 and follow the laughable fractions.
Let me put on my clown nose and get into character. *Honk honk*
If $300 is 5/8 of the remaining money after John bought the radio and presents, we need to figure out what 1/8 of that amount is.
Do you want to hear a joke while we calculate? Why don't scientists trust atoms? Because they make up everything! *Ba-dum-tss*
Alright, so 1/8 of the remaining money is $300 divided by 5, which is $60.
Now, if 1/8 is $60, we simply multiply that by 8 to get the original amount John had. Mathematically amusing, isn't it?
So, $60 multiplied by 8 gives us the grand total of $480.
Voilà! John originally had $480 before he embarked on his spending spree, spreading joy and laughter along the way. *Cue the confetti and circus music*
To find out how much John originally had, let's break down the information step by step:
1. John spent $176 on a radio.
2. Let's assume the remaining amount of money after buying the radio is "X".
3. John spent 6/11 of X on presents for his friends.
4. After spending 6/11 of X, John had (1 - 6/11) = 5/11 of X left.
5. John put 5/8 of this remaining money into his checking account.
6. After putting 5/8 of 5/11 of X into his checking account, John had (1 - 5/8) * 5/11 of X left.
7. This remaining amount is equal to $300, according to the given information.
Therefore, we can set up the equation:
(1 - 5/8) * 5/11 * X = 300
Simplifying the equation,
(3/8) * 5/11 * X = 300
(15/88) * X = 300
Now, we can solve for X,
X = 300 * (88/15)
X ≈ 1,760
So, John originally had $1,760.
To find out how much money John originally had, we will need to work through the problem step by step.
Let's break down the given information:
1. John spent $176 on a radio.
2. After buying the radio, he spent 6/11 of what was left on presents for his friends.
3. The remaining money was then put into his checking account, which is 5/8 of the original amount.
4. Finally, he donated $300 to charity, leaving some money behind.
Let's start from the end and work our way back to find the original amount.
1. John donated $300 to charity, so the money left after putting money in his checking account is $300 more than what he donated.
2. We know that the money left after putting money in the checking account is 5/8 of the original amount.
Let's say the money left after putting money in the checking account was X dollars.
So, we can write the equation: X = (5/8) * Original Amount + $300.
Now let's move back and consider the money left after spending on presents for his friends.
1. John spent 6/11 of what was left on presents for his friends. So, the money left after spending on presents is 5/11 of what was left.
Let's say the money left after spending on presents was Y dollars.
We can write the equation: Y = (5/11) * X.
Finally, let's bring in the information about the money spent on the radio.
1. John spent $176 on the radio, so the money left after buying the radio is $176 more than what was spent.
Let's say the money left after buying the radio was Z dollars.
We can write the equation: Z = Y + $176.
To find out the original amount, we need to solve these equations simultaneously:
Z = Y + $176,
Y = (5/11) * X,
X = (5/8) * Original Amount + $300.
To simplify the problem, let's solve these equations step by step:
1. Substitute the value of Y from the second equation into the first equation:
Z = ((5/11) * X) + $176.
2. Substitute the value of X from the third equation into the above equation:
Z = ((5/11) * ((5/8) * Original Amount + $300)) + $176.
3. Simplify and solve the equation for Z:
Z = (25/88) * Original Amount + (625/11) + $176.
The value of Z represents the money left after buying the radio, spending on presents, and putting money in the checking account. This is the amount that was originally in John's savings account.
Therefore, to find the original amount, we set Z equal to the value of the savings account:
Z = Original Amount.
Now we can solve the equation:
(25/88) * Original Amount + (625/11) + $176 = Original Amount.
Solving this equation will give us the original amount John had in his savings account.