Question 367156
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) {{{G+S = 3500}}}
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) {{{0.15G+0.12S = 480}}}
Now let's replace the G in equation 2) with its equivalent: {{{G = 3500-S}}} which we get from equation 1) by solving for G.
3) {{{0.15(3500-S)+0.12S = 480}}} Simplify and solve for S.
3a) {{{525-0.15S+0.12S = 480}}}
3b) {{{525-0.03S = 480}}} Subtract 525 from both sides.
3c) {{{-0.03S = - 45}}} Finally, divide both sides by -0.03
3d) {{{highlight(S = 1500)}}} This is the number of dollars invested in silver.
{{{G = 3500-S}}}
{{{G = 3500-1500}}}
{{{highlight_green(G = 2000)}}} and this is the number of dollars invested in gold.