There were 3 glasses containing the same volume of liquid. Mr Lee poured 210 ml of the liquid from Glass A into Glass C, and 150 ml of the liquid from Glass B into Glass C. In the end, the ratio of the volume of liquid in Glass A to the volume of liquid in Glass B was 3:8.
A.) What was the final volume of liquid in Glass A?
B.) What was the volume of liquid in each glass at first?
(x-210)/(x-150) = 3/8
8x-1680 = 3x - 450
5x = 1230
x = 246
all glasses had 246 ml at first
246-210 = 36 ml left in A
246-150 = 96 ml left in B
36/96 = 3:8
A.) Well, in order to find the final volume of liquid in Glass A, we need to do a bit of math. We know that the ratio of the volume of liquid in Glass A to the volume of liquid in Glass B is 3:8. Since Glass C received 210 ml from Glass A and 150 ml from Glass B, we can say that the difference in volume between Glass A and Glass B before the transfer was (210 - 150) ml, which is 60 ml. Now, if the ratio of the volume in Glass A to the volume in Glass B is 3:8, we can set up the following equation: 60 / 3 = x / 8, where x represents the final volume of liquid in Glass A. Solving this equation, we find that x = 160 ml. So the final volume of liquid in Glass A is 160 ml.
B.) Now, let's figure out the volume of liquid in each glass at first. Since the final volume of liquid in Glass A is 160 ml and 210 ml was poured into Glass C, we can subtract 210 ml from 160 ml to find that the initial volume of liquid in Glass A was 50 ml. Similarly, since the final volume of liquid in Glass B is 8 times the volume in Glass A, we can divide 160 ml by 8 to find that the initial volume of liquid in Glass B was 20 ml. As for Glass C, we know that 210 ml was poured from Glass A and 150 ml was poured from Glass B, so the initial volume of liquid in Glass C was 210 + 150 ml, which is 360 ml. So the initial volumes of liquid in the glasses were: Glass A = 50 ml, Glass B = 20 ml, and Glass C = 360 ml.
Let's solve this step by step:
Step 1: Set up equations
Let's denote the initial volume of liquid in Glass A as "x" ml, and the initial volume of liquid in Glass B as "y" ml. We know that the final volume of liquid in Glass A is 210 ml less than the initial volume since Mr Lee poured 210 ml into Glass C. So, the final volume of liquid in Glass A can be expressed as "x - 210" ml. Similarly, the final volume of liquid in Glass B is 150 ml less than the initial volume, so it can be expressed as "y - 150" ml.
Step 2: Formulate the ratio equation
According to the given ratio, the volume of liquid in Glass A to the volume of liquid in Glass B is 3:8. So we can write the equation:
(x - 210)/(y - 150) = 3/8
Step 3: Solve the equation
To solve the equation, we can cross-multiply and simplify:
8(x - 210) = 3(y - 150)
8x - 1680 = 3y - 450
8x - 3y = 1680 - 450
8x - 3y = 1230 ... (Equation 1)
Step 4: Simplify the given information
We know that Mr Lee poured 210 ml from Glass A into Glass C and 150 ml from Glass B into Glass C. So, the final volume of liquid in Glass C is the sum of these two amounts, which is 210 ml + 150 ml = 360 ml.
Step 5: Write the equation for Glass C
Since the initial volume of liquid in Glass C was zero (as it was empty initially) and Mr Lee poured 360 ml into it, the final volume of liquid in Glass C can be represented as "360" ml.
Step 6: Simplify the equation for Glass C
The final volume of liquid in Glass C is equal to the sum of the volumes poured from Glass A and Glass B. So we can write the equation:
210 + 150 = 360
Step 7: Solve the equation for Glass C
By simplifying, we have:
360 = 360
This equation satisfies the condition.
Step 8: Solve the equation for Glass A and Glass B
By substituting the final volume of liquid in Glass C into Equation 1, we can solve for Glass A and Glass B:
8x - 3y = 1230
8x - 3(360) = 1230
8x - 1080 = 1230
8x = 1230 + 1080
8x = 2310
x = 2310/8
x = 288.75
Since the volumes of liquid must be in whole numbers, we can round x to the nearest whole number:
x = 289
Step 9: Calculate the final volume of liquid in Glass A and Glass B
The final volume of liquid in Glass A is equal to the initial volume of liquid in Glass A minus the amount poured into Glass C:
Final volume of liquid in Glass A = x - 210
Final volume of liquid in Glass A = 289 - 210
Final volume of liquid in Glass A = 79 ml
The final volume of liquid in Glass B is equal to the initial volume of liquid in Glass B minus the amount poured into Glass C:
Final volume of liquid in Glass B = y - 150
Final volume of liquid in Glass B = 361 - 150
Final volume of liquid in Glass B = 211 ml
So, to summarize:
A.) The final volume of liquid in Glass A is 79 ml.
B.) The initial volume of liquid in each glass was 289 ml for Glass A and 361 ml for Glass B.
To solve this problem, let's break it down step by step.
A.) What was the final volume of liquid in Glass A?
We know that 210 ml of liquid was poured from Glass A into Glass C. Let's assume that the initial volume of liquid in Glass A was x ml.
After pouring 210 ml into Glass C, the volume of liquid remaining in Glass A would be (x - 210) ml.
Based on the given ratio, we can set up the following equation:
(x - 210) / (volume of liquid in Glass B) = 3 / 8
Now, let's find the volume of liquid in Glass B. Since 150 ml was poured from Glass B into Glass C, the remaining volume in Glass B would be (volume of liquid in Glass B - 150) ml.
Substituting these values into the equation, we have:
(x - 210) / ((volume of liquid in Glass B) - 150) = 3 / 8
To find the solution, we need another equation. From the problem statement, we know that the volume of liquid in Glass C is the sum of the volumes poured from both Glass A and Glass B. Hence:
210 + 150 = (volume of liquid in Glass C)
Now, we have two equations with two unknowns. By solving this system of equations, we can find the values of x (the initial volume of liquid in Glass A) and (volume of liquid in Glass B).
B.) What was the volume of liquid in each glass at first?
Using the volume of liquid in Glass A (x) obtained from the previous step, we can determine the initial volumes of liquid in each glass.
Glass A: x ml (initial volume)
Glass B: (volume of liquid in Glass B) ml (initial volume)
Glass C: 210 ml (volume poured from Glass A) + 150 ml (volume poured from Glass B)
Solving the system of equations will give us the final volume in Glass A, providing the answer to question A, and the initial volumes in each glass, answering question B.