Mr. Smith invests a certain amount of money at 8% and twice as much at 5%. If his annual income from the two investments is $720, how much does he have invested at 5%? (in $)
+29 Let the amount of money Mr. Smith invested at \(8\)% be \(m\). This makes the amount of money Mr. Smith invested at \(5\)% equal to \(2m\).
Now we can create an equation:
\($0.08m + 0.05 \cdot $2m = $720\)
Simplifying the equation:
\(0.05 \cdot $2m = $0.1m\).
And the simplified equation:
\($0.08m + $0.1m = $720\)
Adding like terms:
\($0.18m = $720\)
Solving for \(m\):
\({0.18m \over 18} = {720 \over 18}\)
\(0.01m = $40\)
\(0.01m \cdot 100 = 40 \cdot 100\)
\(m = 4000\)
Mr. Smith invested \($4000\) at \(8\)%, so he invested \($8000\) at \(5\)%.
ANSWER: \($8000\).
I hope this is helpful,
Catarina
