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 the tank and the pail. The ratio of the water in the tank to that pail became 7:2.

a. how much water was in the pail at the end?
b.how much water was poured into the pail?

No dude, can you explain how to get 7.7?

To solve this problem, we can set up an equation based on the given information. Let's use the variable 'x' to represent the equal amount of water poured into both the tank and the pail.

Given:
Water in the tank before pouring = 35 gallons
Water in the pail before pouring = 4.5 gallons

After pouring an equal amount ('x') of water into both the tank and the pail, we know that:
Water in the tank after pouring = 35 + x gallons
Water in the pail after pouring = 4.5 + x gallons

We are also given that the ratio of water in the tank to the water in the pail after pouring becomes 7:2. Using this information, we can create an equation:

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

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

Now, let's solve for 'x':

70 + 2x = 31.5 + 7x
70 - 31.5 = 7x - 2x
38.5 = 5x
x = 38.5 / 5
x = 7.7

Now we can answer the questions:

a. The amount of water in the pail at the end is:
4.5 + x = 4.5 + 7.7 = 12.2 gallons

b. The amount of water poured into the pail is:
x = 7.7 gallons

I am afraid that unless you post HOW you receive the answer, your equation really does not help. Unless you mean to say that you would do 35+4.5+2x=3.5 That may make sense, though I am not sure. I will have to check

Oh Wow I am terribly sorry. I just realized how easy that is... Thank you so much!

a. The ratio of water in the tank to the pail is 7:2, which means the total ratio of water is 9 parts. Since there were initially 35 gallons in the tank, the amount of water in each part is 35 ÷ 9 = 3.89 gallons. So, at the end, there would be 2 parts of water in the pail: 2 × 3.89 = 7.78 gallons.

b. Since an equal amount of water was poured into both the tank and the pail, the amount of water poured into the pail would be half of the increase in the pail. The increase in the pail can be found by subtracting the initial amount from the final amount: 7.78 - 4.5 = 3.28 gallons. Therefore, the amount of water poured into the pail would be half of this increase: 3.28 ÷ 2 = 1.64 gallons.

If x gallons were poured, then

(35+x)/(4.5+x) = 7/2
x = 7.7

Now it's easy peasy.

I believe that the answer is actually 7.8 gallons. Let me explain. The x-x cancels out, leaving it as 35/4.5 Dividing that gives you 7.8 gallons.