Alex is painting a house. He uses 1/3 of the paint he bought on the dining room. He uses twice as much on the living room as on the kitchen, where he uses 1 1/2 gallons. He has 1 1/2 gallons of paint left. How much paint did Alex buy?
Let's break down the information given step by step:
1. Alex uses 1 1/2 gallons of paint on the kitchen.
2. He uses twice as much on the living room as on the kitchen, which means he uses 1 1/2 x 2 = 3 gallons of paint on the living room.
3. He uses 1/3 of the paint he bought on the dining room, so if we let 'x' represent the amount of paint he bought, he uses x / 3 gallons of paint on the dining room.
4. The total amount of paint used on the kitchen, living room, and dining room is 1 1/2 + 3 + (x/3) = 1 1/2 + 3 + x/3 = 1 1/2 + 3 + (1/3)x.
5. We are told that Alex has 1 1/2 gallons of paint left, so the total amount of paint he bought subtracted by the amount he used is 1 1/2 - (1 1/2 + 3 + (1/3)x) = 1 1/2 - 1 1/2 - 3 - (1/3)x = -3 - (1/3)x.
6. We know that he has 1 1/2 gallons of paint left, so -3 - (1/3)x = 1 1/2.
7. To solve for 'x', we can add 3 to both sides of the equation: -3 + 3 - (1/3)x = 1 1/2 + 3.
8. Simplifying further, we have: -(1/3)x = 4 1/2.
9. To eliminate the fraction, we multiply both sides of the equation by -3: -3 * (-(1/3)x) = -3 * (4 1/2).
10. This gives us: x = -13 1/2.
From the calculation, we find that Alex bought -13 1/2 gallons of paint. However, it is not possible to buy a negative amount of paint, so there may be an error in the given information. Please double-check the problem statement for accuracy.
To find out how much paint Alex bought, we need to find the total amount of paint he used.
Let's start by finding the amount of paint he used in the kitchen. We are given that he used 1 1/2 gallons of paint in the kitchen.
Next, we need to find the amount of paint he used in the living room. We are told that he used twice as much paint in the living room as in the kitchen. Since he used 1 1/2 gallons in the kitchen, he used 1 1/2 * 2 = 3 gallons in the living room.
Now, let's calculate the total amount of paint he used so far. He used 1 1/2 gallons in the kitchen and 3 gallons in the living room, so the total amount of paint he used is 1 1/2 + 3 = 4 1/2 gallons.
Finally, we need to determine how much paint he used on the dining room. We are told that he used 1/3 of the paint he bought on the dining room. Since he used 4 1/2 gallons in total, we can calculate the amount of paint he bought by multiplying the total amount used by 3.
(4 1/2) x 3 = 13 1/2
So, Alex bought 13 1/2 gallons of paint.
bought x gallons
dining room = (x/3) gallons
kitchen = 1.5 gallons
living rm = 3 gallons
leftover = 1.5 gallons
so
(x/3) + 6 = x
6 = 2 x/3
x = 9 gallons