Uncle Joe made chocolate chip cookies. Eric ate fifty percent of them right away. Ryan ate fifty percent of what was left. Ten cookies remain. How many cookies did Uncle Joe make?
x(1-.5)(1-.5) = 10
x = 40
Would have been more interesting if both reductions had not been 50%
Let's work through this step by step.
Step 1: Eric ate fifty percent of the cookies right away. So, let's calculate how many cookies were left after Eric ate his share. If we let x represent the original number of cookies Uncle Joe made, then after Eric ate 50% of them, (x - 0.5x) cookies remained. Simplifying, we get 0.5x cookies remaining.
Step 2: Ryan then ate fifty percent of what was left. So, let's calculate how many cookies were left after Ryan ate his share. If we let y represent the number of cookies remained after Eric's consumption, then after Ryan ate 50% of them, (y - 0.5y) cookies remained. Simplifying, we get 0.5y cookies remaining.
Step 3: We are given that ten cookies remain. Using this information, we can set up an equation to represent the number of cookies remaining after Ryan ate his share: 0.5y = 10.
Step 4: Solving for y, we divide both sides of the equation by 0.5: y = 10/0.5 = 20.
Step 5: Now that we know y represents the number of cookies remaining after Eric ate his share, we can substitute this value back into the equation from Step 1 to find the original number of cookies Uncle Joe made: 0.5x = y = 20.
Step 6: Solving for x, we divide both sides of the equation by 0.5: x = 20/0.5 = 40.
Therefore, Uncle Joe made 40 cookies.
To find the number of cookies Uncle Joe made, we need to work backwards from the remaining ten cookies.
Let's start with Eric. We know he ate fifty percent (or half) of the cookies right away. So, if we represent the initial number of cookies as "x," Eric ate 0.5x (half of x) cookies.
Next, we need to find out how many cookies were left after Eric had his share. Since Ryan then ate fifty percent of what was left, the remaining amount can be calculated by subtracting Eric's share from the initial number of cookies: x - 0.5x = 0.5x. So, 0.5x cookies were left after Eric ate.
We're given that ten cookies remain, so we can set up the equation: 0.5x = 10. We need to solve for x.
To isolate x, we can divide both sides of the equation by 0.5:
(0.5x) / 0.5 = 10 / 0.5
This simplifies to: x = 20.
Therefore, Uncle Joe made a total of 20 cookies.