If six cookies cost the same as 2 brownies, and four brownies cost the same as 10 cupcakes, how many cupcakes can Bob buy for the price of eighteen cookies?

Bob can buy 15 cupcakes for the price of 18 cookies.

Step-by-step explanation:

Assume the cost of a cookie is $x, the cost of a brownie is $y and the cost of a cupcake is $z. It is given that 6 cookies and 2 brownies cost the same, so 6x = 2y, take this as equation 1. It is also given that 4 brownies cost the same as 10 cupcakes, so 4y = 10z, take this as equation 2. If we divide equation 2 by 2 we get, 2y = 5z so that the y value is the same as equation 1 and we can equate equation 1 and 3. We get 6x = 2y = 5z, 6x = 5z, dividing both sides by 5, we get 1.2x = z. We need to calculate how many cupcakes Bob can buy for the price of 18 cookies, So we must find the z value when the x = 18. If we multiply 1.2 with 15 we get 18 so we the last equation is multiplied with 12 so that 18x = 15z. 18 cookies and 15 cupcakes cost the same.