Question

A tank and a pail contain a total of 5136 milliliter of water. Jacob pours 314 milliliters of water from the pail into tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Answer 1

To find the initial amount of water in the pail, set up a system of equations based on the total volume and the information provided after transferring some water. Solve the equations to obtain the initial quantity of 957 milliliters in the pail.

Step-by-step explanation:

A student posed a problem: A tank and a pail contain a total of 5136 milliliters of water. Jacob pours 314 milliliters of water from the pail into the tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Let's denote the initial amount of water in the tank as T milliliters and in the pail as P milliliters. According to the given information, the combined quantity of water in both is 5136 milliliters:

T + P = 5136

After transferring 314 milliliters from the pail to the tank, the tank now has T + 314 milliliters, and the pail has P - 314 milliliters. It is also given that the water in the tank is now 7 times the water left in the pail:

(T + 314) = 7*(P - 314)

Now, we have a system of two equations:

By solving these equations, we can find the initial amount of water in the pail, P. First, modify the second equation to isolate T:

T = 7P - 2206 - 314

T = 7P - 2520

Next, substitute the expression for T from the second equation into the first equation and solve for P:

7P - 2520 + P = 5136

8P = 5136 + 2520

8P = 7656

P = 7656 / 8

P = 957 milliliters

Initially, there were 957 milliliters of water in the pail.

Answer 2

let t = mL water in tank
let p = mL water in the pail

Start with the first statement
t + p = 5136

Second statement
7(p - 314) = t + 314

Use substitution to re-write as one equation in one variable.

t = 5136 - p

7(p - 314) = 5136 - p + 314
7p - 2198 = 4822 - p
7p + p = 4822 + 2198
8p = 7020
p = 7020/8
p = 877.5 mL