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Find the approximate value of (?) in the...

Find the approximate value of (?) in the following questions.
`?% "of" {(26.03)^(2) - 19.023 xx 3.99} = 1818.014`

A

311

B

315

C

332

D

303

Text Solution

AI Generated Solution

The correct Answer is:
To find the approximate value of the question mark (?) in the equation: \[ ?\% \text{ of } \{(26.03)^2 - 19.023 \times 3.99\} = 1818.014 \] we will follow these steps: ### Step 1: Approximate the values We will approximate the numbers involved in the equation: - \( 26.03 \approx 26 \) - \( 19.023 \approx 19 \) - \( 3.99 \approx 4 \) - \( 1818.014 \approx 1818 \) So, we rewrite the equation as: \[ ?\% \text{ of } \{(26)^2 - (19 \times 4)\} = 1818 \] ### Step 2: Calculate \( (26)^2 \) Now, calculate \( (26)^2 \): \[ (26)^2 = 676 \] ### Step 3: Calculate \( 19 \times 4 \) Next, calculate \( 19 \times 4 \): \[ 19 \times 4 = 76 \] ### Step 4: Substitute and simplify Now substitute these values back into the equation: \[ ?\% \text{ of } \{676 - 76\} = 1818 \] Calculate \( 676 - 76 \): \[ 676 - 76 = 600 \] So now we have: \[ ?\% \text{ of } 600 = 1818 \] ### Step 5: Convert percentage to fraction Convert the percentage into a fraction: \[ \frac{?}{100} \times 600 = 1818 \] ### Step 6: Solve for ? To isolate ?, we can multiply both sides by \( 100 \): \[ ? \times 600 = 181800 \] Now, divide both sides by 600: \[ ? = \frac{181800}{600} \] ### Step 7: Calculate the value Now perform the division: \[ ? = 303 \] ### Conclusion Thus, the approximate value of ? is: \[ \boxed{303} \]
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