Ms. Wilson invested ​$23,000 in two​ accounts, one yielding 7​% interest and the other yielding 12​%.

Question

If she received a total of​ $2,210 in interest at the end of the​ year, how much did she invest in each​ account?

Answer 1

Let x represent the amount (in dollars) invested in the 7% interest account. Then 23,000 - x is the amount invested in the 12% interest account. At the end of the year, the first account earned (.07)x in interest, and the other account earned (.12)(23,000 - x) in interest. Thus

.07x + .12(23,000 - x) = 2,210

.07x + .12(23,000) - .12x = 2,210

-.05x + 2760 = 2,210

-.05x = -550

x = 11,000

Therefore, Ms. Wilson invested $11,000 in the first account and $23,000 - $11,000 = $12,000 in the second account.