Question

the combined age of april and laura is 23 years. laura's age is two years more than half of april's age. what is laura's age

Answer 1

Laura's age is 9 years.

Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

Convert statement into algebraic expression:

Half of April's age = $\frac{x}{2}$

2 years more than half of April's age = $\frac{x}{2}+2$

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

$\Rightarrow \ \ x+(\frac{x}{2}+2) =23$

$\Rightarrow \ \ x+\frac{x}{2}+2 =23$

$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23$

To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23$

$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23$

Denominators are same, now add the fractions.

$\Rightarrow \ \ \frac{2x+x+4}{2} =23$

Do cross multiplication.

$\Rightarrow \ \ 2x+x+4=23\times2$

$\Rightarrow \ \ 3x=46-4$

$\Rightarrow \ \ 3x=42$

$\Rightarrow \ \ x=14$

Aprils's age = 14 years

Laura's age = $\frac{14}{2}+2$

                    = 7 + 2

Laura's age = 9

Hence Laura's age is 9 years.