If A is 150% of B and B is 40% of C and A + B + C is 20 then find the value of 2B + 3C – 5A.

Options

A. 10
B. 12
C. 8
D. 15

Answer

To solve the problem step by step, we will define the relationships given in the question and then calculate the required expression.

### Step 1: Define the relationships
We know:
- A is 150% of B
- B is 40% of C

From the above, we can express A and B in terms of C.

### Step 2: Express A and B in terms of C
1. Since B is 40% of C:
\[ B = 0.4C \]

2. Since A is 150% of B:
\[ A = 1.5B = 1.5(0.4C) = 0.6C \]

### Step 3: Substitute A and B into the equation A + B + C = 20
Now we substitute A and B into the equation:
\[ A + B + C = 20 \]
Substituting the values:
\[ 0.6C + 0.4C + C = 20 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ (0.6C + 0.4C + 1C) = 20 \]
This simplifies to:
\[ 2C = 20 \]

### Step 5: Solve for C
Now, divide both sides by 2:
\[ C = 10 \]

### Step 6: Find B and A using the value of C
1. Substitute C back into the equation for B:
\[ B = 0.4C = 0.4(10) = 4 \]

2. Substitute C back into the equation for A:
\[ A = 0.6C = 0.6(10) = 6 \]

### Step 7: Calculate the expression 2B + 3C - 5A
Now we need to find the value of \(2B + 3C - 5A\):
\[ 2B + 3C - 5A = 2(4) + 3(10) - 5(6) \]

### Step 8: Perform the calculations
Calculate each term:
1. \(2B = 2(4) = 8\)
2. \(3C = 3(10) = 30\)
3. \(5A = 5(6) = 30\)

Now substitute these values back into the expression:
\[ 2B + 3C - 5A = 8 + 30 - 30 \]
This simplifies to:
\[ 2B + 3C - 5A = 8 \]

### Final Answer
The value of \(2B + 3C - 5A\) is \(8\).

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