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OPTIONAL EC) My father's age divided by 5 is equal to my brother's age divided by 3. My brother is 3 years older than me. My father's age is 3 less than 2 times my age. How old is my father? 34

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Let's call "F" the age of the father

"B" the age of the brother

and "Y" your age

so we can create the followig equations from each sentence:

"My father's age divided by 5 is equal to my brother's age divided by 3"

F / 5 = B / 3

"My brother is 3 years older than me."

B = Y + 3

"My father's age is 3 less than 2 times my age."

F = 2 Y - 3

So now we replace in the very first equation we wrote, F with " 2 Y - 3" as per what the last equation gave us. And also we replace B with "Y + 3" as per what the second equation gave us. Therefore we end up with the following equation (with one only variable "Y"):

(2 Y - 3) / 5 = (Y + 3) / 3

we multiply both sides by "15" in order to cancel out both denominators (3 and 5):

3 (2 Y - 3) = 5 (Y + 3)

use distributive property

6 Y - 9 = 5 Y + 15

subtract 5 Y from both sides

6 Y - 5 Y - 9 = 15

Y - 9 = 15

add 9 to both sides

Y = 15 + 9 = 24

so Y = 24, that means that father's age is:

F = 2 Y - 3 = 2 (24) - 3 = 48 - 3 = 45

So the father's age is 45 years old.

User Guy Sirton
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