Alex is painting a house. He uses 1/3 of the paint he bought on the dining room. He uses twice as much as the living room as on the kitchen, when he uses 1-1/2 gallons. He has 1-1/2 gallons of paint left. How much paint did Alex buy?
looks like 9 gallons to me.
To find out how much paint Alex bought, let's go step by step.
Let x be the total amount of paint Alex bought.
From the given information, we know that he used 1/3 of the paint on the dining room. Therefore, the amount of paint used on the dining room is (1/3) * x = x/3.
Next, we are told that he used twice as much on the living room as on the kitchen, which used 1-1/2 gallons. So, the amount of paint used on the living room is 2 * (1-1/2) gallons = 2 * 1.5 = 3 gallons.
We are also given that he has 1-1/2 gallons of paint left. So, the remaining amount of paint is 1-1/2 gallons = 1.5 gallons.
Since Alex used a total of x/3 gallons on the dining room and 3 gallons on the living room, the remaining amount (1.5 gallons) can be expressed as:
x - (x/3 + 3) = 1.5
To solve this equation, we can combine like terms:
(2/3)x - 3 = 1.5
Next, we can isolate x by adding 3 to both sides:
(2/3)x = 4.5
Then, multiply both sides of the equation by 3/2 to cancel out the fraction:
(2/3)x * (3/2) = 4.5 * (3/2)
Giving us:
x = 6.75
Therefore, Alex bought 6.75 gallons of paint.