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:
[tex](x - 5)^2=5x+11[/tex]
To find Zeba's age now, solve the equation for x.
Expand the brackets:
[tex]\implies x^2-10x+25=5x+11[/tex]
Subtract 5x from both sides:
[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]
[tex]\implies x^2-15x+25=11[/tex]
Subtract 11 from both sides:
[tex]\implies x^2-15x+25-11=11-11[/tex]
[tex]\implies x^2-15x+14=0[/tex]
Factor the found quadratic
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-14x-x+14=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-14)-1(x-14)=0[/tex]
Factor out the common term (x - 14):
[tex]\implies (x-1)(x-14)=0[/tex]
Apply the zero product property:
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-14)=0 \implies x=14[/tex]
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.
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