Last summer, Betty earned $4200 by painting houses. She invested some of the money in a savings account that paid 3.5%/year and the rest in a government bond that paid 4.5%/year. After one year, she has earned $174 in interest. How much did she invest at each rate?
Let's assume Betty invests x amount of money in the savings account at 3.5% interest rate.
The amount she invests in the government bond at 4.5% interest rate will be $4200 - x.
The interest earned from the savings account will be x * 3.5/100.
The interest earned from the government bond will be ($4200 - x) * 4.5/100.
According to the given information, the total interest earned is $174.
Therefore, we have the equation:
(x * 3.5/100) + (($4200 - x) * 4.5/100) = $174
3.5x/100 + 4.5(4200 - x)/100 = 174
3.5x + 18900 - 4.5x = 17400
4.5x - 3.5x = 18900 - 17400
x = 1500
Hence, Betty invested $1500 in the savings account and $4200 - $1500 = $<<4200-1500=2700>>2700 in the government bond. Answer: \boxed{1500,2700}.