There were 35 gallons of water in a tank and 4.5 gallons of water in a pail. An equal amount of water was poured into a tank and the pail. The ratio of the water in the tank to the pail became 7:2.

a) How much water was in the pail in the end?
b) How much water was poured into the pail?

Your answer was stupid

If the amount poured is x gallons, then

(35-x)/(4.5+x) = 7/2

find x, and the rest is easy.

To solve this problem step-by-step, we can start by setting up equations based on the information given.

Let's denote the amount of water poured into both the tank and the pail as "x" gallons.

We know that initially, there were 35 gallons of water in the tank and 4.5 gallons of water in the pail. After pouring an equal amount of water into both, the ratio of the water in the tank to the pail became 7:2.

a) To find out how much water was in the pail in the end:
- We can set up the equation: (4.5 + x) / (35 + x) = 2/7
- Cross-multiplying, we get: 7(4.5 + x) = 2(35 + x)
- Expanding both sides of the equation: 31.5 + 7x = 70 + 2x
- Subtracting 2x from both sides: 31.5 + 5x = 70
- Subtracting 31.5 from both sides: 5x = 38.5
- Dividing both sides by 5, we find: x = 7.7

Therefore, at the end, there were 4.5 + 7.7 = 12.2 gallons of water in the pail.

b) To determine how much water was poured into the pail:
- We already calculated that x = 7.7 gallons.

Therefore, 7.7 gallons of water were poured into the pail.

To solve this problem, we need to set up equations based on the given information and then solve for the unknown quantities.

Let's use variables to represent the unknowns:
Let x be the amount of water poured into both the tank and the pail.
Let p be the final amount of water in the pail.

a) We are looking for the final amount of water in the pail, which is represented by the variable p.

From the given information, initially, there were 35 gallons of water in the tank. We poured an equal amount of water into both the tank and the pail, so the tank now has 35 + x gallons of water.

Initially, there were 4.5 gallons of water in the pail. We also poured an equal amount into the pail, so the pail now has 4.5 + x gallons of water.

According to the problem, the ratio of the water in the tank to the pail became 7:2. So we have the equation:

(35 + x)/ (4.5 + x) = 7/2

To solve this equation, we'll cross-multiply and solve for x:
2*(35 + x) = 7*(4.5 + x)

Simplify the equation:
70 + 2x = 31.5 + 7x

Move the variables to one side and constants to the other:
7x - 2x = 70 - 31.5
5x = 38.5

Divide both sides by 5:
x = 38.5 / 5
x = 7.7

Now we have found the value of x, which represents the amount of water poured into both the tank and the pail.

b) We are looking for the amount of water poured into the pail, which is also represented by x.

Therefore, the amount of water poured into the pail is 7.7 gallons.

To find the final amount of water in the pail, we substitute the value of x back into the equation for the pail's water:

p = 4.5 + x
p = 4.5 + 7.7
p = 12.2

Therefore, the amount of water in the pail in the end is 12.2 gallons.