Question

If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?​

Answer 1

Answer:

I am not 100% confident, but I think that she is 11.

Step-by-step explanation:

Answer 2

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

$(x - 5)^2=5x+11$

To find Zeba's age now, solve the equation for x.

Expand the brackets:

$\implies x^2-10x+25=5x+11$

Subtract 5x from both sides:

$\implies x^2-10x+25-5x=5x+11-5x$

$\implies x^2-15x+25=11$

Subtract 11 from both sides:

$\implies x^2-15x+25-11=11-11$

$\implies x^2-15x+14=0$

Factor the found quadratic

To factor a quadratic in the form $ax^2+bx+c$, find two numbers that multiply to $ac$ and sum to $b$, then rewrite $b$ as the sum of these two numbers:

$\implies x^2-14x-x+14=0$

Factor the first two terms and the last two terms separately:

$\implies x(x-14)-1(x-14)=0$

Factor out the common term (x - 14):

$\implies (x-1)(x-14)=0$

Apply the zero product property:

$\implies (x-1)=0 \implies x=1$

$\implies (x-14)=0 \implies x=14$

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

Learn more about quadratic equations here:

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