Quiz 6

Solution:

Consider:
Blue Glass = B Full and B Half
Yellow Glass = Y Full and Y Half
Red Glass = R Full and R Half

Simple Method:

Just consider a number for a glass and apply it to equations and find out if they are equals. For example, if you consider that a full glass has a value of 4, then the half one of the same color will be worth 2. Now, if you solve the equation, the result should be equal to the given number on the right-hand side. With this method, one could figure out the values of each set of colored glasses.
Now put those values in the fourth equation and find out the answer. [Check the 4th equation below]

Mathematical Method:
Using math, one could determine the answer as follows:

1st Equation:

⇒ B Full + B Half + B Full = 15
If Full Glass = B, then Half Glass = B/2
⇒ B + B/2 + B = 15
(To cancel out the half, multiply the above equation with 2 and we will get)
⇒ 2B + B + 2B = 15 × 2
⇒ 5B = 30
⇒ B = 30/5 = 6
Therefore: B Full = 6, so B Half = 3

2nd Equation:

⇒ Y Full – Y Half + B Full = 10
⇒ Y – Y/2 + B = 10
⇒ Y – Y/2 = 10 – B (Put the value of B)
⇒ Y – Y/2 = 10 – 6
⇒ Y – Y/2 = 4
⇒ 2Y – Y = 4 × 2
⇒ Y = 8
⇒ So, Y Full = 8 and Y Half = 4

3rd Equation:

⇒ R + R – (R/2) = 06
⇒ 2R + 2R – R = 06 × 2
⇒ 4R – R = 12
⇒ 3R = 12
⇒ R = 12/3 = 4
So, R Full = 4 and R Half = 2

Now we have the value of Red, Blue and Yellow Glass:

Blue: B Full = 6 and B Half = 3
Yellow: Y Full = 8 and Y Half = 4
Red: R Full= 4 and R Half = 2

4th Equation:

⇒ B Half + (B Half + R Half) × Y Half = ??
⇒ 3 + (3 + 2) × 4 = ??
⇒ 3 + (5) × 4 = ??
⇒ 3 + 20 = ??
⇒ 23 Answer
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