YoU order 6 pizza & you eat 2/3 of one pizza before your guest arrived. Each one of your guest eat 1/4 of pizza & left with 5/6 of pizza. How many guest did you invited?
To solve this problem, let's break it down step by step.
Step 1: Calculate how much pizza was initially eaten before the guests arrived.
You ordered 6 pizzas and ate 2/3 of one pizza. To find out how much pizza was eaten before the guests arrived, we multiply the total number of pizzas ordered by the fraction of one pizza eaten:
Initial pizza eaten = (6 pizzas) * (2/3) = 12/3 = 4 pizzas
Step 2: Calculate how much pizza was left for the guests.
Since you ordered 6 pizzas initially and ate 4 pizzas, the amount of pizza left for the guests is:
Pizza left = 6 pizzas - 4 pizzas = 2 pizzas
Step 3: Determine how much pizza each guest ate and how much was left.
Each guest ate 1/4 of a pizza, but there was 5/6 of a pizza left. So, we need to solve the equation:
(1/4) * x = 5/6
To solve this equation, we'll multiply both sides by 4/1 to isolate the variable:
x = (5/6) * (4/1) = 20/6 = 10/3
Step 4: Interpret the result.
From the equation above, x represents the number of guests you invited, and we found that x = 10/3. However, we cannot have fractional guests, so we need to round up to the nearest whole number because you can't have a fraction of a guest.
Therefore, you invited 4 guests because rounding 10/3 to the nearest whole number gives us 4.
So, you invited 4 guests to share the pizza.