Question

Josh has some money. He uses 5/8 of his money to buy 10 cakes. With the rest of the money, he can buy 3 cakes and 9 cookies. A cake costs $4.50 more than a cookie. How much money did he spend on cakes?

Answer 1

Let Josh has 8x dollars
Because he uses 5/8 of his money to buy 10 cakes.
5/8 * 8x = 5x dollars can buy 10 cakes
So a cake is 5 * 10 = 0.5x dollars
A cake costs $4.50 more than a cookie
So a cookie is 0.5x - 4.50 dollars
The rest of the money is 8x - 5x = 3x dollars
With the rest of the money, he can buy 3 cupcakes and 9 cookies
So 3x = 3 * (0.5x) + 9 (0.5x - 4.50)
3x = 1.5x + 4.5x - 40.5
3x = 6x - 40.5
-3x = -40.5
x = 13.5
So a cake is 0.5x = 0.5 * 13.5 = 6.75 dollars
Josh buy 10 + 3 = 13 cakes in total
So he spent 13 * 6.75 = 87.75 dollars on cakes