SOLUTION: The sum of Anne's income for one year on 1,500 dollars at simple interest and on 2,000 dollars for two years at simple interest is 480 dollars. If the interest rates are interchang
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Question 1182895: The sum of Anne's income for one year on 1,500 dollars at simple interest and on 2,000 dollars for two years at simple interest is 480 dollars. If the interest rates are interchanged, she would receive 455 dollars. Find the interest rate of the 1,500 dollars account.
Let x = rate on $1500 account
Let y = rate on $2000 account
Note the problem doesn't ask us to find both x and y; we only need to find x.
The interest from $1500 at rate x, plus the interest from $2000 at rate y, is $480: [1]
The interest from $1500 at rate y, plus the interest from $2000 at rate x, would have been $455: [2]
Solve the pair of equations [1] and [2] simultaneously by your favorite method.
With both equations in Ax+By form, I would use elimination; but it's up to you. In this problem I would definitely use elimination, because we only need to solve for x.
Multiply each equation by an appropriate constant so the y coefficients are the same:
Subtract one equation from the other, eliminating y; then solve the resulting equation for x.
