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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 $720, how much does he have invested at 5%? (in$)

Mar 10, 2020

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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:
$$0.08m + 0.1m = 720$$

$$0.18m = 720$$

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: $$8000$$.