Question

Diego's sister is twice his age minus 9 years. She is also as old as half the sum of the ages of Diego and both of his 12-year-old twin brothers. Write and solve an equation to find the ages of Diego and his sister.

Answer 1

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 $2x-9$.  

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:          

$2x-9=\frac{x+12+12}{2}$

Let us solve for x:

$2x-9+9=\frac{x+24}{2}+9$

$2x=\frac{x+24}{2}+\frac{2*9}{2}$

$2x=\frac{x+24}{2}+\frac{18}{2}$

$2x=\frac{x+24+18}{2}$

$2x=\frac{x+42}{2}$

$2*2x=\frac{x+42}{2}*2$

$4x=x+42$

$4x-x=x-x+42$

$3x=42$

$\frac{3x}{3}=\frac{42}{3}$

$x=14$

Therefore, Diego's age is 14 years.

$\text{His sister's age}=2x-9$

$\text{His sister's age}=2(14)-9$

$\text{His sister's age}=28-9$

$\text{His sister's age}=19$

Therefore, his sister's age is 19 years.

Answer 2

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