Hi Amanda,
Let x = amount at 8%
Let y = amount at 10%
(x + y +300) = amount at 13% (300 more that the amounts at 8% and 10% combined
839 = .08*x + .1y + .13(x + y +300)
7500 = x + y + (x+y+300)
now lets simplify each equation
839 = .21x + .23y + 39
7200 = 2x + 2y
Lets get rid of the decimals in the first equation - we will mutliply by 100
83900 = 21x + 23y +3900
80000 = 21x + 23y
and now lets multipy each equation by a number that will make of the the terms the same so we can get rid of it
160000 = 42x + 46y (multiplied equation by 2
151200 = 42x + 42y (multiplied by 21
now subtract to solve for y
8800 = 4y
y = 2200 (amount at 10%
now find x
7200 = 2x + 2y
7200 = 2x + 4400
2800 = 2x
x = 1400 (amount at 8%
x + y + 300
1400 + 2200 + 300 = 3900 (amount at 13%
now you can check it
1400(.08) + 2200(.1) + 3900(.13)
112 + 220 + 507
= 839 and it all checks out
Hope this helps