Last year sarah invested money in two accounts. the first account had an interest rate of 2%2% and the second account had an interest rate of 5%5%. if she invested $100$⁢100 more in the first account than the second and her total interest income was $422$⁢422, how much did she invest at each rate?

the amount invested in first account = $6,100

and, the amount invested in second account = $6,000

Explanation:

Data provided:

Interest rate of first account = 2% = 0.02

Interest rate of second account = 5% = 0.05

Let the amount invested in second account be 'a'

thus,

the amount invested in first account = a + $100

Now,

Interest = principle × interest rate

therefore,

For first account

Interest = ( a + $100 ) × 0.02 = 0.02a + 2

and

for second account = a × 0.05

also,

0.02a + 2 + ( a × 0.05 ) = $422

or

0.07a + 2 = $422

or

0.07a = $420

or

a = $6,000

Hence,

the amount invested in first account = a + $100 = $6,000 + $100 = $6,100

and, the amount invested in second account = a = $6,000