Word problems w/ substitution/elimination

Question

a company invests in 2 accounts. An account that provides more cash flow freedoms pays 2.2% annual interest and the other pays 7.5% annual interest. If the company invests $5000 less in the 2.2% account than in the other account and makes $2218 total interest income in a year, how much is invested at each rate?

Answer 1

24000 at 7.5%

19000 at 2.2%

Your substitution given above

x = is invested at 7.5%

x - 5000 = is invested at 2.2%

Your total interest earned is given $ 2218

First thanks so much for spotting my typo the complete solution is below

.075x + 0.022(x - 5000)= 2218

Multiply to remove the parentheses first

0.075x + 0.022x - 110 = 2218

Combine like terms

0.097x - 110 = 2210

Add 110 to both sides of the equation

0.097x = 2328

Divide both sides by 0.097

x = 2328/.097

x = 24000 for the amount invested at 7.5%

x - 5000 = 24000 - 5000 = 19000 for the amount invested at 2.2%

Checking

0.075x + 0.022(x - 5000) = 2218

0.075(24000) + 0.022(24000 - 5000) = 2218

0.075(24000) + 0.022(19000) = 2218

1800 + 418 = 2218

2218 = 2218

I hope you find this useful and thanks again for catching my typo and getting back to me.