Question

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 that day.

Answer 1

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

Answer 2

He sold 88 plain cakes and he decorated 8 cakes.

Explanation: