Need to solve an equation

[jackcheang]

Three years hence a boy’s age will be 4 times the square of what it was 11 years ago. Find his present age.

 

[Deleted member 4993]

Three years hence a boy’s age will be 4 times the square of what it was 11 years ago. Find his present age.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[stapel]

Three years hence a boy’s age will be 4 times the square of what it was 11 years ago. Find his present age.

a) Pick a variable (link) for the boy's age now.
b) Create an expression (link), in terms of the variable in (a), for his age in three years.
c) Create an expression, in terms of the variable in (a), for his age eleven years ago.
d) Create an expression, in terms of the expression in (c), for the square of his age eleven years ago.
e) Create an expression, in terms of the expression in (d), for four times the square of his age eleven years ago.
f) Create an equation, in terms of the expressions in (a) and (e), for the equality of his age in three years and four times the square of his age eleven years ago.
g) Solve the equation (link).

If you get stuck, please reply showing your progress in following the step-by-step instructions. Thank you!

 

[whiz]

solution to Need to solve an equation

let x be the boy's age today.
x + 3 represents his age three yrs hence.
x - 11 represents his age 11 yrs ago.

the equation is

x + 3 = 4(x - 11)^2

solving for x,

x + 3 = 4(x - 11)^2
x + 3 = 4(x^2 - 22x + 121) expanding the right side of the equation
x + 3 = 4x^2 - 88x + 484 distributive property
0 = 4x^2 - 89x + 481 equating to 0
(x - 13)(4x - 37) factoring
x = 13, x = 37/4

thus, the boy is 13 yrs old today. we reject the value 37/4 o r 9.25 because this does not make a sense on the phrase "11 yrs ago". to check,

he is 13 yrs old today. 3 yrs hence, he will be 16 yrs old.
11 yrs ago he was 2 yrs old. square that age, 2^2 = 4.

his age 3 yrs hence (16) is 4 times his age 11 yrs ago (4).

i hope this helps!