David loves Oreos and has a special way of enjoying them. He starts by taking a bite out of an Oreo, which leaves him with 5/6 of the original cookie. Then, he takes a portion of the remaining cookie, represented by (1/5 * x), where x is the number of Oreos he initially had. After that, he adds 30 to this portion. Finally, David multiplies this sum by 5/6 and adds 15 to the result. The final expression is equal to 70. How many Oreos did David initially had?

1 answer

Let's work step by step to set up the equation.

1. David takes a bite out of an Oreo, which leaves him with 5/6 of the original cookie. This means he has (5/6)*x Oreos remaining.

2. David takes a portion of the remaining cookie, represented by (1/5 * x), where x is the number of Oreos he initially had. After that, he adds 30 to this portion. So, (1/5 * x) + 30 is the new portion.

3. Finally, David multiplies this sum by 5/6 and adds 15 to the result. The final expression is (5/6)*((1/5 * x) + 30) + 15 = 70.

Let's simplify this expression:

(5/6)*((1/5 * x) + 30) + 15 = 70
(5/6)*(x/5 + 30) + 15 = 70
(5/6) * (x + 150) + 15 = 70
(5/6) * x + (5/6) * 150 + 15 = 70
(5/6) * x + (5/6) * 150 = 55
(5/6) * x + 125 = 55
(5/6) * x = 55 - 125
(5/6) * x = -70

To solve for x, let's multiply both sides of the equation by 6/5:

(6/5)*(5/6)*x = (6/5)*(-70)
x = -84

Since the number of Oreos cannot be negative, it means that David initially had 84 Oreos.