1) If a car travels 357 miles and uses 21 gallons of gas, how many miles does it average per gallon of gas?
2) 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?
357mi/21gal = 357/21 m i/gal = 17 mi/gal
dr = 1/3 p
lr = 2k
k = 3/2
p - dr-lr-k = 3/2
p - p/3 - 2(3/2) - 3/2 = 3/2
p = 9
1) Well, let's do the math. If the car traveled 357 miles and used 21 gallons of gas, the average would be 357/21 = 17 miles per gallon. Or you could say it's about the same as a jogger running a marathon and then needing a nap.
2) Ah, the world of house painting, where gallons of paint and fractions come together in harmony. So, Alex used twice as much paint on the living room as on the kitchen, where he used 1 1/2 gallons. That means he used 1 1/2 x 2 = 3 gallons on the living room. We also know that he used 1/3 of the paint on the dining room. So, if he had 1 1/2 gallons left after all this painting extravaganza, he must have bought 1 1/2 + 3 + (1/3) x (total paint) = 1 1/2. Phew, that's a lot of math for a paint job. But hey, at least Alex didn't run out of paint!
1) To find the average miles per gallon of gas, divide the total number of miles traveled by the total number of gallons of gas used.
Average miles per gallon = 357 miles / 21 gallons
= 17 miles per gallon
2) Let's break down the information given in the problem step-by-step.
- Alex 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.
Let's find out how much paint Alex used in each room.
1) Kitchen: Alex used 1 1/2 gallons of paint.
2) Living room: He used twice as much on the living room as on the kitchen, which is 1 1/2 * 2 = 3 gallons.
3) Dining room: He used 1/3 of the paint he bought on the dining room, which is (1/3) * x where x is the amount of paint Alex bought.
Now, we can set up the equation:
1 1/2 + 3 + (1/3)x = x - 1 1/2
Simplifying the equation:
4 1/2 + (1/3)x = x - 1 1/2
Multiplying everything by 6 to clear the fractions:
27 + 2x = 6x - 9
Subtracting 2x from both sides:
27 = 4x - 9
Adding 9 to both sides:
36 = 4x
Dividing both sides by 4:
x = 9
Therefore, Alex bought 9 gallons of paint.
1) To find the number of miles the car averages per gallon of gas, we can divide the total miles traveled by the total gallons of gas used.
To do this calculation, we can use the formula:
Average miles per gallon = Total miles traveled / Total gallons of gas used
In this case, the car travels 357 miles and uses 21 gallons of gas. Therefore, the calculation would be:
Average miles per gallon = 357 miles / 21 gallons
By dividing 357 by 21, we find that the car averages approximately 17 miles per gallon of gas.
2) To determine how much paint Alex bought, we can add up the amount of paint he used in each room and the amount of paint he has left.
Alex used 1/3 of the paint on the dining room, which means he used (1/3) * Total paint.
For the kitchen, Alex used 1 1/2 gallons of paint.
For the living room, he used twice as much as the kitchen, so he used 2 * 1 1/2 = 3 gallons.
And Alex has 1 1/2 gallons of paint left.
So, to find the total paint Alex bought, we need to sum up all these amounts:
Total paint = (1/3) * Total paint + 1 1/2 + 3 + 1 1/2
Simplifying the equation, we have:
Total paint = (1/3) * Total paint + 6
Now, let's solve for Total paint. To do this, we first subtract (1/3) * Total paint from both sides of the equation:
(2/3) * Total paint = 6
Then, we multiply both sides of the equation by (3/2) to isolate Total paint:
Total paint = 6 * (3/2)
By calculating 6 * (3/2), we find that Alex bought a total of 9 gallons of paint.