Question 1105577
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Let x be the number of decorative 2x2 inch tiles
Let y be the number of plain 6x6 inch tiles<br>
In square inches, the area of each decorative tile is 4; the area of each plain tile is 36; the area of the whole floor is 60*96 = 5760:
{{{4x+36y = 5760}}}
(1) {{{x+9y = 1440}}}  [divide by the common factor of 4]<br>
The cost of each decorative tile is $1.25; the cost of each plain tile is $0.75; the total cost is $246:
{{{1.25x+.75y = 246}}}
(2) {{{5x+3y = 984}}}  [multiply by 4 to get rid of the decimals]<br>
The problem asks for x, the number of decorative tiles she can get; so use elimination with equations (1) and (2) to eliminate y.  Multiply equation (2) by 3 and subtract equation (1):
{{{15x+9y = 2952}}}
{{{x+9y = 1440}}}
{{{14x = 1512}}}
{{{x = 1512/14 = 108}}}