(.06*a)+(.08*b)=$220.00
find a and b, a and b equal $3000.
Obviously a and b do NOT equal $3000. If they did,
you would already have the solution to the problem.
Stated properly, a PLUS b equals $3000. We now
have two equations that we can solve simultaneously.
(.06*a)+(.08*b)=$220.00
and
a + b = $3000
We can eliminate b, leaving us with a.
100 * (0.06a + 0.08b) = 100 * $220
1) 6a + 8b = $22000
We want the b term in the second equation
to be equal to the b term in the first equation.
8 * (a + b) = 8 * $3000
2) 8a + 8b = $24000
Now, we subtract equation 1 from equation 2.
8a + 8b = $24000
-(6a + 8b = $22000)
------------------------------
2a = $2000
a = $1000
Substitute the value of a into one of the
original equations.
a + b = $3000
$1000 + b = $3000
b = $2000
Now, substitute both a and b into the
other equation given for the problem, to
verify the solution.
(.06*a)+(.08*b)=$220.00
0.06 * $1000 + 0.08 * $2000 = $220
$60 + $160 = $220
$220 = $220