SOLUTION: Where do I start? OLD COINS: A salesperson used her $3,500 year-end bonus to purchase some old coins, with hopes of earning 15% annual interest on the gold coins and 12% annual i

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Question 367156: Where do I start?
OLD COINS: A salesperson used her $3,500 year-end bonus to purchase some old coins, with hopes of earning 15% annual interest on the gold coins and 12% annual interest on the silver coins. If she saw return on her investment of $480 the first year, how much did she invest in each type of coin?
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
You can start by assigning variables to the unknown quantities, the invested amounts in gold and in silver.
Let G = the number of dollars invested in gold and S = the number of dollars invested in silver.
The sum of these two amounts is given as $3,500.00, so you can write:
1)
Now we must find an equation for the amount of interest earned.
The interest earned on the gold investment is 15%(G) and the interest earned on the silver investment is 12%(S), and the sum of these two amounts is given as $480.00
So, after changing the percents to their decimal equivalents, you can write the equation:
2)
Now let's replace the G in equation 2) with its equivalent: which we get from equation 1) by solving for G.
3) Simplify and solve for S.
3a)
3b) Subtract 525 from both sides.
3c) Finally, divide both sides by -0.03
3d) This is the number of dollars invested in silver.

and this is the number of dollars invested in gold.