A man spends 1/5 of his income on food and 1/3 of the remainder on his car.If he then has 286.00 left what is his income
i - (i / 5) - (4 i / 15) = 286
15 i - 3 i - 4 i = 286 * 15
1-1/5 = 5/5-1/5 = 4/5 remainder.
4/5-1/3 = 12/15-5/15 = 7/15 remains.
7x/15 = 286
X =
I dont understand
1-1/5 for food = 4/5 left
1/3 of 4/5 on the car = 4/15
1/5 for food + 4/15 on the car = 7/15 spent
For the value of what is left
1-7/15 of the total amount = 286
8/15 of x = 286
X = 286*15/8
X = 536.25
To break it down step by step:
Let's call the man's income "x".
1. He spends 1/5 of his income on food, so he has 4/5 of his income remaining.
2. Of that remaining amount, he spends 1/3 on his car. 1/3 of 4/5 is (1/3) x (4/5) = 4/15.
3. He has now spent 1/5 on food and 4/15 on his car, which adds up to 1/5 + 4/15 = 7/15 of his income.
4. We are told that he has 286 left from the remaining amount after spending on food and car.
5. So the equation becomes: (8/15)x = 286 (since he has 8/15 of his income remaining)
6. Solving for x, we get x = 286 x (15/8) = 536.25.
Therefore, the man's income is $536.25.
To solve this problem, we can follow these steps:
Step 1: Determine the portion of income spent on food.
The man spends 1/5 of his income on food, which can be represented as 1/5 * I, where I represents his income.
Step 2: Calculate the remaining income.
The remainder can be found by subtracting the amount spent on food from his income:
Remaining income = I - (1/5 * I) = (5/5 - 1/5) * I = (4/5) * I.
Step 3: Determine the portion of the remainder spent on his car.
The man spends 1/3 of the remainder on his car, which can be represented as 1/3 * (4/5 * I).
Step 4: Calculate the remaining income after car expenses.
The remaining income after car expenses can be found by subtracting the amount spent on the car from the remainder:
Remaining income = (4/5 * I) - (1/3 * (4/5 * I)) = (4/5 * I) - (4/15 * I)
= (12/15 * I) - (4/15 * I) = (8/15 * I).
Step 5: Calculate the final income amount.
We know that the remaining income is $286.00. So, we have the equation:
(8/15 * I) = 286.00
To solve for I, we can multiply both sides by (15/8):
I = 286.00 * (15/8)
I = 534.37
Therefore, the man's income is approximately $534.37.