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?
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.
To find the number of Oreos David initially had, let's break down the given information step-by-step:
1. David takes a bite out of an Oreo, leaving him with 5/6 of the original cookie. So, if x is the number of Oreos he initially had, after taking a bite, he would have 5/6 * x Oreos.
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 taking this portion, he adds 30 to it. So, the expression becomes: (1/5 * x) + 30.
3. Finally, David multiplies this sum by 5/6 and adds 15 to the result. The final expression is equal to 70. So, the equation becomes: ((5/6) * ((1/5 * x) + 30)) + 15 = 70.
Let's solve this equation to find the value of x:
((5/6) * ((1/5 * x) + 30)) + 15 = 70
Simplifying the equation:
(5/6) * ((1/5 * x) + 30) + 15 = 70
(5/6) * (1/5 * x) + (5/6) * 30 + 15 = 70
(1/6 * x) + (5/2) + 15 = 70
(1/6 * x) + 5/2 + 15 = 70
(1/6 * x) + 25/2 = 70
Multiplying all terms by 6 to eliminate the fraction:
x + 75 = 420
Subtracting 75 from both sides:
x = 420 - 75
x = 345
Therefore, David initially had 345 Oreos.