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Nico is saving money for his college education. He invests some money at 9​%, and ​$1700 less than that amount at 5%. The investments produced a total of ​$223 interest in 1 yr. How much did he invest at each​ rate?

He invested $___ at 9% and $___ at 5%.

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Let [tex] x_1 [/tex] the amount of money invested at 9% and [tex] x_2 [/tex] the amount of money invested at 5%. The amount invested at 5% ([tex] x_2 [/tex]) is 1700$ less than the amount invested at 9%  ([tex] x_1 [/tex]) it means:
[tex]x_1 - 1700 = x_2[/tex] (equation 1)
The investments produced 223$ which means:
[tex]\frac{9}{100} x_1 + \frac{5}{100} x_2 = 223[/tex]. (equation 2)
We use the first equation to eliminate [tex] x_2 [/tex] from equation 2:
[tex]\frac{9}{100} x_1 + \frac{5}{100} (x_1-1700) - = 223\\ \frac{9}{100} x_1 + \frac{5}{100} x_1- \frac{5}{100}1700 - = 223\\ \frac{14}{100} x_1 = 308\\ X_1 = 308*\frac{100}{14} = 2200\\ X_2 = X_1-1700 = 2200-1700 = 500[/tex]

He invested 2200$ at 9% and 500$ at 5%.

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