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

Diego's age is 14 years.

His sister's age is 19 years.

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=(x+12+12)/(2)`

Let us solve for x:

`2x-9+9=(x+24)/(2)+9`

`2x=(x+24)/(2)+(2*9)/(2)`

`2x=(x+24)/(2)+(18)/(2)`

`2x=(x+24+18)/(2)`

`2x=(x+42)/(2)`

`2*2x=(x+42)/(2)*2`

`4x=x+42`

`4x-x=x-x+42`

`3x=42`

`(3x)/(3)=(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

Diego is 14 years old.

Sister is 19

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