John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold all but 4. His sales that day totaled $800.
He sold _ plain cakes and _ decorated cakes.
+129840 Call the number of plain cakes he sold = x and the number of decorated cakes he sold = y
So....since he had 4 left, he must have sold a total of 96 of both
x + y = 96 → y = 96 - x (1)
And the price per plain cake * the number he sold + price of the decorated cake * the number he sold = total sales
So
8x + 12y = 800 (2)
Subbing (1) into (2), we have that
8x + 12 (96 - x) = 800 simplify
8x + 1152 - 12x = 800
-4x + 1152 = 800 subtract 1152 from both sides
-4x = -352 divide both sides by -4
x = 88 = the number of plain cakes he sold
And 96 - x = 96 - 88 = 8 = the number of decorated cakes he sold
