Last month, Nate spent 12% of his paycheck on car repairs and 25% of the remainder on food. He gave $1,320 of the remaining money to his parents and then bought a computer on sale. If the usual price of the computer was $825 and the discount was 20%, how much money did Nate have in the beginning?
cost of computer = .8(825) = 660
original amount of money --- x
12x/100 + .25(88/100)x +1320 + 660 = x
34x/100 - x = -1980
66x-100x = -198000
x = 3000
check:
car repairs = .12(3000) = $360.00
leaves --- 2640.00
food = .25(2640) = 660
amount to parents = 1320.00
computer = 660
sum = 360.00+660.00+1320.00+660.00 = 3000
He had $3000 at the beginning
Well, let's do some clown math to figure out how much money Nate had in the beginning.
First, we know that Nate spent 12% of his paycheck on car repairs. That means he had 88% of his paycheck left.
Then, he spent 25% of the remaining money on food. So now he has 75% of that 88% left.
Next, he gave $1,320 to his parents, leaving him with the remaining money.
Now, let's figure out the cost of the computer after the discount. The discount was 20%, so the computer cost 80% of the usual price. That means Nate paid $825 x 0.80 = $660 for the computer.
Finally, we can add up everything Nate spent: car repairs + food + parents + computer = $1,320 + $660 = $1,980.
Since $1,980 is the remaining money after all his expenses, we can calculate Nate's paycheck as the total money divided by 75% (since that's what he had left after food): $1,980 / 0.75 = $2,640.
So, Nate had $2,640 in the beginning. Now go tell him to stop spending so much on car repairs and food!
Let's break down the problem step-by-step:
Step 1: Calculate the amount of money Nate spent on car repairs.
Since Nate spent 12% of his paycheck on car repairs, we can calculate this by finding 12% of the total amount:
12% of his paycheck = 0.12 * paycheck
Step 2: Calculate the remaining money after car repairs.
To find the remaining money, we need to subtract the amount spent on car repairs from Nate's paycheck:
Remaining money = paycheck - (0.12 * paycheck)
Step 3: Calculate the amount of money Nate spent on food.
Since Nate spent 25% of the remainder on food, we can calculate this by finding 25% of the remaining money:
Amount spent on food = 0.25 * remaining money
Step 4: Calculate the new remaining money after spending on food.
To find the new remaining money, we need to subtract the amount spent on food from the previous remaining money:
New remaining money = remaining money - (0.25 * remaining money)
Step 5: Calculate the amount Nate gave to his parents.
Since Nate gave $1,320 to his parents, the new remaining money becomes:
New remaining money = new remaining money - $1,320
Step 6: Calculate the discounted price of the computer.
Since the discount on the computer was 20%, the discounted price can be calculated as:
Discounted price = $825 - (0.20 * $825)
Step 7: Calculate the final remaining money after buying the computer.
To find the final remaining money, we need to subtract the discounted price of the computer from the new remaining money:
Final remaining money = new remaining money - discounted price
Step 8: Calculate the initial amount of money Nate had.
To find the initial amount of money Nate had, we need to add the final remaining money to the amount spent on car repairs, food, and the amount given to his parents:
Initial amount of money = remaining money + amount spent on food + $1,320 + discounted price + $825
Now we can calculate the answer by following these steps.
To find out how much money Nate had in the beginning, we can work backwards from the information given.
Let's start by finding out how much money Nate had left after he bought the computer on sale. The usual price of the computer was $825, but the discount was 20%. To calculate the discount, we multiply the usual price by the discount rate: 825 * 0.20 = $165. So, Nate paid $825 - $165 = $660 for the computer.
Now let's backtrack further. We know that Nate gave $1,320 of the remaining money to his parents. So, after buying the computer, he had $660 - $1,320 = -$660 left.
Since Nate's balance is negative, it means that the remaining money after buying the computer was insufficient to cover the amount he gave to his parents. Therefore, we can conclude that Nate had less than $660 after spending on car repairs and food.
Now, let's go back to the information about Nate's spending. Last month, Nate spent 12% of his paycheck on car repairs and 25% of the remainder on food. This implies that 12% + 25% = 37% of his paycheck was spent.
Let's assume that x is Nate's paycheck. Then we have the equation:
0.37x = $660
To find x, we divide both sides of the equation by 0.37:
x = $660 / 0.37
Calculating this gives us x ≈ $1783.78.
Therefore, Nate had approximately $1,783.78 in the beginning.