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1 year ago

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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 a

ctually age. What is her age now?

2 answers:

8090 [49]1 year ago

6 0

Answer:

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

Step-by-step explanation:

RSB [31]1 year ago

5 0

Answer:

14 years old

Step-by-step explanation:

<u>Define the variable</u>

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

<u>Create an equation</u> using the give information and the variable x:

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

To find Zeba's age now, <u>solve the equation for x</u>.

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:

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

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

<u>Factor the found quadratic</u>

To factor a quadratic in the form $ax^2+bx+c$ <em>, </em>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 <u>zero product property</u>:

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

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

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 <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.

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

<u>Check</u>

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 <u>actual age is 14 years old</u>.

Learn more about quadratic equations here:

brainly.com/question/27956741

brainly.com/question/27947331

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