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 that in 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?

Question

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 that in 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?

Answer 1

X gal. added to each container.

(35 + x)/(4.5 + x) = 7/2.
Cross-multiply:
70 + 2x = 31.5 + 7x,

Answer 2

please show all your work

Answer 3

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Answer 4

WhaT don't you understand abouat Steve's explanation?

Answer 5

To solve this problem, we'll use the following steps:

Step 1: Understand the problem.
The problem states that there were 35 gallons of water in the tank and 4.5 gallons of water in the pail. An equal amount of water was poured into both the tank and the pail, making the ratio of water in the tank to water in the pail 7:2. We need to find the amount of water in the pail in the end (part a) and the amount of water poured into the pail (part b).

Step 2: Define the variables.
Let's define the amount of water poured into the tank and the pail as 'x'.

Step 3: Set up the equations.
The first equation represents the initial amount of water in the tank and pail:
35 + 4.5 = 39.5 gallons

Now, let's consider the ratio. The ratio of water in the tank to water in the pail after pouring an equal amount of water can be represented as:
(35 + x) / (4.5 + x) = 7/2

Step 4: Solve the equations.
To solve the equation, we can cross-multiply:
2(35 + x) = 7(4.5 + x)
70 + 2x = 31.5 + 7x

Next, we'll isolate the variable 'x' by subtracting 2x from both sides:
70 = 31.5 + 5x

Then, subtract 31.5 from both sides:
70 - 31.5 = 5x
38.5 = 5x

Finally, divide both sides by 5 to find the value of 'x':
38.5 / 5 = x
x ≈ 7.7 gallons

Step 5: Answer the questions.
(a) To find the amount of water in the pail in the end, we add the initial amount of water (4.5 gallons) to the amount poured into the pail (x):
4.5 + 7.7 ≈ 12.2 gallons

Therefore, there are approximately 12.2 gallons of water in the pail in the end.

(b) The amount of water poured into the pail is equal to the value of 'x', which we found to be approximately 7.7 gallons.

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