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Max
07-17-2013, 02:06 PM
SAT math word problem

I need help with the following age word problem:
"Four years ago, John was half as old as Ricky is now. If Ricky is five years older than John, how old is Jim now?"

Thanks!!;)

Oliver
07-17-2013, 02:27 PM
SAT math word problem

"Four years ago, John was half as old as Ricky is now. If Ricky is five years older than John, how old is Jim now?"

Age problems ussually include the present ages of two or more people, in addition to their ages at particular past or future times. The key to solving these problems is to translate the sentences into equations using appropriate variables for the ages.

Let J and R be the ages of John and Ricky, respectively, today.

"Four years ago, John was half as old as Ricky is now": J-4=\frac{R}{2}

"If Ricky is five years older than John":R=J+5

Therefore, we have to solve the following simultaneous equations:

\begin{cases} J-4=\frac{R}{2} \\ R=J+5 \end{cases}

\begin{cases} R=2J-8 \\ R=J+5 \end{cases}

\begin{cases} J+5=2J-8 \\ R=J+5 \end{cases}

\begin{cases} J=13 \\ R=13+5=18 \end{cases}

So, John is now 13 years old and Ricky is now 18 years old.;););)

Max
07-17-2013, 02:27 PM
Thank you Oliver!!