Question 1188799
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A bank lends two people a total of $b. The first person pays x% interest and the second person pays y% interest. 
The amount of interest received by the bank is the same for each loan. How much was loaned at x%
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Let "a" be the amount loaned at x%, in dollars.

Then the amount loaned at y% was (b-a) dollars.


Write this equation as you read the problem


    {{{(x/100)*a}}} = {{{(y/100)*(b-a)}}}.    (1)


In this problem , b, x and y are given value (in symbolic form). The unknown is the value of "a".


From equation (1)


    ax = y*(b-a),

    ax = yb - ya

    ax + ay = yb

    a*(x+y) = yb

    a = {{{(yb)/(x+y)}}}.


<U>ANSWER</U>.  The amount loaned at  x%  was  {{{(yb)/(x+y)}}}.
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Solved.