A woman invests a total of $20,000 in two accounts, one paying 2.5% and the other paying 8% simple interest per year. Her annual interest is $830. How much did she invest at each rate?

Let's have a variable for each rate

x = account 1 (2.5% rate of interest)

y = account 2 (8% rate of interest)

The formulas we need are:

0.025x + 0.08y = 830 (amount of interest paid)

x + y = 20 000 (combined amount invested)

To solve we will use substitution (isolate for one variable and plugging into the other formula):

x + y = 20 000

x = 20 000-y

0.025x + 0.08y = 830

0.025 (20 000-y) + 0.08y = 830

500-0.025y+0.08y=830

500+0.055y=830

0.055y=330

y=6000

Now that we know y (the 2nd account) = $6000 we need to find x. We do this by using the previous formula.

x = 20 000-y

x=20 000 - 6000

x=14000

She invested $14 000 at a 2.5% interest rate and $6 000 at a 8% interest rate.

*Notes:

the percentages were converted into decimal form

you check your answer by plugging the numbers back into the 2 formulas we made