Answer:
Diego is 14 years old.
Sister is 19
Step-by-step explanation:
x = Diego's age
x + 24
2x-9 = 2
First to get rid of the fraction we multiply each side by 2
2(2x-9) = 2((x+24)/2)
4x-18 = x+24
The we isolate x
4x-18 = x+24
-x+18 -x+18
3x = 42 Now we divide each side 3
3 3
x = 14
So Diego is 14
Now we can solve for his sister. We can use one of the two equations from earlier to do this.
Plug 14 in for x and then solve for his sister
2(14)-9
28-9
19
His sister is 19
Answer:
Diego's age is 14 years.
His sister's age is 19 years.
Step-by-step explanation:
Let d represent Diego's age.
We have been given that Diego's sister is twice his age minus 9 years.
The age of Diego's sister would be [tex]2x-9[/tex].
We are also told that she is also as old as half the sum of the ages of Diego and both of his 12-year-old twin brothers. We can represent this information in an equation as:
[tex]2x-9=\frac{x+12+12}{2}[/tex]
Let us solve for x:
[tex]2x-9+9=\frac{x+24}{2}+9[/tex]
[tex]2x=\frac{x+24}{2}+\frac{2*9}{2}[/tex]
[tex]2x=\frac{x+24}{2}+\frac{18}{2}[/tex]
[tex]2x=\frac{x+24+18}{2}[/tex]
[tex]2x=\frac{x+42}{2}[/tex]
[tex]2*2x=\frac{x+42}{2}*2[/tex]
[tex]4x=x+42[/tex]
[tex]4x-x=x-x+42[/tex]
[tex]3x=42[/tex]
[tex]\frac{3x}{3}=\frac{42}{3}[/tex]
[tex]x=14[/tex]
Therefore, Diego's age is 14 years.
[tex]\text{His sister's age}=2x-9[/tex]
[tex]\text{His sister's age}=2(14)-9[/tex]
[tex]\text{His sister's age}=28-9[/tex]
[tex]\text{His sister's age}=19[/tex]
Therefore, his sister's age is 19 years.
