Respuesta :
Answer:
Step-by-step explanation:
Let your number be X. To increase X by 40% we can multiply it by 1.4, let's call this new number Y.
So Y = X * 1.4
Now to decrease Y by 40% we can multiply it by 1 - .4 = .6. Lets call this new number C.
So C = Y *.6 = (X * 1.4) * .6 = X * (1.4 * .6) = X * .84.
Therefore, C = .84 * X.
So we can see C is 84% of X, or 16% less than X.
Thus, if you increase a number by 40% then decrease it by 40%, the net percentage is -16% .
Final result in terms of 'x' will be → 0.75x
Conversion of verbal statement to algebraic expression:
- Select the variables given in the verbal statement first.
- Form the algebraic expression as per verbal statement given in the question.
Let the number = x
As per first statement → "A number 'x' is decreased by 40%"
Algebraic expression for the statement → (x - 40% of x)
→ (x - 0.4x)
→ 0.6x
Second statement → "Then increased by 25%"
Algebraic expression for the statement → (0.6x + 25% of 0.6x)
→ [tex](0.6x+\frac{25}{100}\times 0.6x)[/tex]
→ [tex](0.6x+0.15x)[/tex]
→ [tex]0.75x[/tex]
Therefore, final result in terms of x will be (0.75x).
Learn more about the algebraic expression here,
https://brainly.com/question/561132?referrer=searchResults
