Danny had a sum of money. He spent $315 on a mobile phone and 3/5 of the remaining money on a headphone. He then had 1/10 of the sum of money left. How much money did Danny have at first?
Well, let's use our math skills while also adding a touch of humor.
So, if Danny had a sum of money and spent $315 on a mobile phone, we now need to figure out the remaining amount.
Let's call the remaining amount "X." Now, Danny spent 3/5 of the remaining money on a headphone. So, we can say that the remaining money after buying the mobile phone is (2/5)X.
According to the given information, the remaining money after buying the headphone is 1/10 of the original sum of money.
So, (2/5)X = (1/10) of the original amount.
Let's solve this equation together. Simplifying it, we get (2/5)X = (1/10)X. Now, by multiplying both sides of the equation by 10, we have 4X = X.
But that doesn't mean Danny is some kind of magical money duplicator! It's just a mathematical trick here.
So, let's solve for X. Dividing both sides of the equation by X, we get 4 = 1.
Well, that's not possible, unless we're in some parallel universe where mathematical rules don't apply.
So, there must be an error in the information provided. It seems like something went dollars up at some point. Please double-check the numbers, and let's give it another go!
Let's call the amount of money Danny had at first "x".
After he spent $315 on a mobile phone, he had x - 315 left.
He then spent 3/5 of that money on a headphone, which means he had 2/5 of it left. So:
2/5(x - 315) = 1/10x
Multiplying both sides by 10 to get rid of the fraction:
4(x - 315) = x
Expanding the brackets:
4x - 1260 = x
Subtracting x from both sides:
3x = 1260
Dividing by 3:
x = 420
So Danny had $420 at first.
Let's break down the problem step by step to find the solution.
1. Danny spent $315 on a mobile phone. Let's denote the remaining money as X.
Remaining money = Total money - Money spent on a mobile phone
X = Total money - $315
2. Danny then spent 3/5 of the remaining money on a headphone. Let's denote the money spent on a headphone as Y.
Money spent on a headphone = (3/5) * Remaining money
Y = (3/5) * X
3. After spending money on the headphone, Danny had 1/10 of the sum of money left. Let's denote the remaining money as Z.
Remaining money = (1/10) * Total money
Z = (1/10) * Total money
Now we need to find the total amount of money Danny had at first. To do that, we will set up an equation based on the given information.
From step 1: X = Total money - $315
From step 2: Y = (3/5) * X
From step 3: Z = (1/10) * Total money
Since Z represents the remaining money, we can equate it to X after the headphone was purchased:
Z = X
Now, let's substitute the values:
(1/10) * Total money = X
Substituting X from step 1:
(1/10) * Total money = Total money - $315
Now, we can solve for the total amount of money (Total money):
(1/10) * Total money = Total money - $315
Multiply both sides by 10 to eliminate the fraction:
Total money = 10 * (Total money - $315)
Simplify:
Total money = 10 * Total money - $3150
Total money - 10 * Total money = -$3150
-9 * Total money = -$3150
Divide both sides by -9:
Total money = -$3150 / -9
Total money = $350
Therefore, Danny had $350 at first.
To find out how much money Danny had originally, we need to work through the given information step by step.
Let's start by figuring out how much money Danny had left after buying the mobile phone. We know Danny spent $315 on the phone, so we subtract that from the original amount of money:
Remaining money = Original amount of money - Money spent on mobile phone
Next, we are told that Danny spent 3/5 of the remaining money on a headphone. To find out how much money Danny had left after buying the headphone, we multiply the fraction by the remaining money:
Money spent on headphone = (3/5) * Remaining money
Finally, we are told that Danny had 1/10 of the original sum of money left. So, we can express this as:
Money left = (1/10) * Original amount of money
Now, let's put all the information together and solve the problem.
1. Remaining money = Original amount of money - Money spent on mobile phone
2. Money spent on headphone = (3/5) * Remaining money
3. Money left = (1/10) * Original amount of money
Since we know the values of money spent on the phone and money left, we can substitute them into the equations:
1. Remaining money = Original amount of money - $315
2. Money spent on headphone = (3/5) * Remaining money
3. (1/10) * Original amount of money = Money left
From equation 3, we can rewrite Money left in terms of the original amount of money:
Money left = (1/10) * Original amount of money
Money left = (1/10) * (Original amount of money - $315)
Now that we have an expression for Money left, we can substitute this value into equation 2:
Money spent on headphone = (3/5) * Remaining money
Money spent on headphone = (3/5) * [(1/10) * (Original amount of money - $315)]
We can simplify this further:
Money spent on headphone = (3/50) * (Original amount of money - $315)
Now we have an expression for the money spent on the headphone.
To find the original amount of money, we need to solve the equation:
Remaining money = Money left + Money spent on headphone
Substituting the values:
Original amount of money - $315 = (1/10) * (Original amount of money - $315) + (3/50) * (Original amount of money - $315)
Now we can solve this equation to find the original amount of money.