Question 1163060
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For tutor @MathTherapy....<br>
(1) I firmly agree that the problem should be solved using a single variable.<br>
(2) Check your solution where you factor out the LCM of 15....<br>
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Let the number of suits be x.<br>
The cost of each suit is {{{1620/x}}}<br>
The sale price of each suit is {{{1620/x+15}}}<br>
When (x-9) suits have been sold, the total sales is equal to the original cost:<br>
{{{(x-9)(1620/x+15) = 1620}}}
{{{(x-9)((1620+15x)/x) = 1620}}}
{{{(x-9)(1620+15x) = 1620x}}}
{{{(x-9)(108+x) = 108x}}}
{{{x^2+99x-972 = 108x}}}
{{{x^2-9x-972 = 0}}}
{{{(x-36)(x+27) = 0}}}
{{{x = 36}}} (ignore the negative solution)<br>
ANSWERS:<br>
He bought x=36 suits<br>
The amount he paid for each one was $1620/x = $1620/36 = $45<br>
CHECK: (x-9) suits, sold at 1620/x+15 each, should equal 1620:<br>
{{{(x-9)(1620/x+15) = 27(1620/36+15) = 27(45+15) = 27(60) = 1620}}}<br>