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Difficulty: MediumDecimal Operations

An engineer uses the formula V=V0−r×t+CV = V_0 - r \times t + C to calculate the final volume of fluid in a tank in liters. If the initial volume V0=12.4V_0 = 12.4, the rate r=2.5r = 2.5, the time t=3.2t = 3.2, and a correction factor C=4.8C = 4.8, what is the final volume VV?

  1. A
    16.4
  2. 9.2Answer
  3. C
    -0.4
  4. D
    36.48

Answer

9.2
To find the final volume, substitute the values into the formula to get 12.4−2.5×3.2+4.812.4 - 2.5 \times 3.2 + 4.8. According to the order of operations, the multiplication must be evaluated first: 2.5×3.2=8.02.5 \times 3.2 = 8.0. Substituting this back gives 12.4−8.0+4.812.4 - 8.0 + 4.8. Performing the remaining operations from left to right, first subtract (12.4−8.0=4.412.4 - 8.0 = 4.4), and then add (4.4+4.8=9.24.4 + 4.8 = 9.2).

Step-by-Step Solution

1
Substitute the given values into the formula.
V=12.4−2.5×3.2+4.8V = 12.4 - 2.5 \times 3.2 + 4.8
This sets up the arithmetic expression that needs to be evaluated.
2
Apply the order of operations (PEMDAS) by performing the multiplication first.
2.5×3.2=8.02.5 \times 3.2 = 8.0
Multiplication takes precedence over addition and subtraction.
3
Rewrite the expression with the product and perform the subtraction (working left to right).
12.4−8.0=4.412.4 - 8.0 = 4.4
Addition and subtraction are evaluated from left to right in the order they appear.
4
Perform the final addition step.
4.4+4.8=9.24.4 + 4.8 = 9.2
This yields the final evaluated volume.

Key Concept

Applying the order of operations (PEMDAS) to expressions containing decimals, ensuring proper place-value alignment during addition and subtraction.
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Topics

Decimal Operations

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