Question

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?

Answer 1

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

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.