Respuesta :
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 = [tex]\frac{x}{2}[/tex]
2 years more than half of April's age = [tex]\frac{x}{2}+2[/tex]
Combined age of April and Laura = 23
⇒ April's age + Laura's age = 23
[tex]$\Rightarrow \ \ x+(\frac{x}{2}+2) =23[/tex]
[tex]$\Rightarrow \ \ x+\frac{x}{2}+2 =23[/tex]
[tex]$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23[/tex]
To add the fractions make the denominators same.
Multiplying 2 on both numerator and denominator of unlike terms, we get
[tex]$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23[/tex]
[tex]$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23[/tex]
Denominators are same, now add the fractions.
[tex]$\Rightarrow \ \ \frac{2x+x+4}{2} =23[/tex]
Do cross multiplication.
[tex]$\Rightarrow \ \ 2x+x+4=23\times2[/tex]
[tex]$\Rightarrow \ \ 3x=46-4[/tex]
[tex]$\Rightarrow \ \ 3x=42[/tex]
[tex]$\Rightarrow \ \ x=14[/tex]
Aprils's age = 14 years
Laura's age = [tex]\frac{14}{2}+2[/tex]
= 7 + 2
Laura's age = 9
Hence Laura's age is 9 years.
