Desiree invested some money at 9% and $100 less than three times the amount at 7%. Her total annual interest was $83. How much did she invest at each rate?

Answer 1

9 % = 9 / 100 = 0.09

7 % = 7 / 100 =0.07

x = the amount of money

$100 less then three times the amount = 3 x - 100

x * 0.09 + ( 3 x - 100 ) * 0.07 = 83

0.09 x + 3 x * 0.07 - 100 * 0.07 = 83

0.09 x + 0.21 x - 7 = 83

0.3 x - 7 = 83

0.3 x = 83 + 7

0.3 x = 90

x = 90 / 0.3

x = 300

3 x - 100 = 3 * 300 - 100 = 900 - 100 = 800

$300 with interest 9% and $800 with interest 7%

$300 * 0.09 + $800 * 0.07 = $27 + $56 = $83