Question 1108965
let x = the interest rate on the 19000 dollar investment.


let y = the interest rate on the 5000 dollar investment.


you get 19000 * x - 5000 * y = 617


that means that the annual interest on the 19000 dollar investment is 617 dollars higher than the annual interest on the 5000 dollar investment.


you are given that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.


.3% is equal to .003.


this results in x = y + .003


you have 2 equations that need to be solved simultaneously.


they are:


19000 * x - 5000 * y = 617
x = y + .003


replace x in the first equation with the equivalent value of y + .003 from the second equation to get:


19000 * (y + .003) - 5000 * y = 617


simplify to get 19000 * y + 57 - 5000 * y = 617.


combine like terms to get:


14000 * y + 57 = 617.


subtract 57 from both sides to get:


14000 * y = 560.


solve for y to get y = 560 / 14000 = .04.


you have y = .04 and x = .043, since x is .003 more than .04.


go back to your original problem to see if it makes sense when x = .043 and y = .04


the original problem says that the difference between the interest on the 19000 dollar investment  and the interest on the 5000 dollar investment is 617 dollars.


the original problem also states that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.


19000 * .043 - 5000 * .04 is equal to 617 dollars, confirming the solution is correct.


the solution is that the interest rate on the 19000 investment is 4.3% and the interest rate on the 5000 dollar investment is 4.0%.


note that .3% = .003


the percent rate divided by 100 equal the rate.