age promblems

[flowe2]

the promblem is juan is 5 yrs older than his brother carlos. five yrs ago juan was twicce as old as carlos how old is each now

 

[dvdrnkn]

Please explain more

I have tried to use your example and cannot come up with an answer by using algebra. I know their ages, not how to write the formula. Thank you for your help.

 

[tkhunny]

I have tried to use your example and cannot come up with an answer by using algebra. I know their ages, not how to write the formula. Thank you for your help.

The equation writing is what you are supposed to be learning. Letting the notation help you is a bridge you must cross.

"Juan is 5 yrs older than his brother, Carlos. Five yrs ago, Juan was twice as old as Carlos. How old is each now?"

Rule #1 - Name Stuff. If you do not do this, you are not getting it. You are not using the logical organization the notation provides. If you are having trouble deciding what to name, as youself, "What does it want?" In this case, it wants both ages. Name those.

J = Juan's Age Now
C = Carlos's Age Now

Time to Translate into the new language just created by the naming conventions just established.

"Juan is 5 yrs older than his brother, Carlos."

J = C + 5

You must stare at this until you see the complete relationship between the words and the symbols. In particular, note how compact the notation is when compared to the words. Alarms should go off in your head. I'm pretty sure Carlos is at least 0 years of age. This makes Juan at least 5. Keep this in mind.

More translating!

"Five yrs ago"

Juan was J - 5 and Carlos was C - 5

Some alarms should go off in your head. C-5? J-5? These things had better be non-negative. A moment ago, I said Carlos must be at least 0 years of age. Well, now we must change that to at least 5 years old, otherwise we could not subtract 5 years! C-5 MUST be 0 or greater! If you get as a final answer, C = 3, something is seriously wrong. Keep your eyes open for these "Domain Issues". Also, this makes Juan at least 10. ALWAYS keep this sort of information in mind. It will keep you from wandering off.

"Five yrs ago, Juan was twice as old as Carlos."

J - 5 = 2(C - 5)

Again, stare at this until you se the relationship between the words and hte symbols. Don't forget to refer to the clearly written definitions.

Okay, we're out of information to translate. It is hoped that we can create a solution from what we have translated. Let's collect...

J = C + 5
J - 5 = 2(C - 5)


Can you solve these two equations simultaneously for J and C? Don't forget to check what we know.