Aaron. Bob and Carl sold pies at a funfair. Aaron sold 5/8 of the total number of pies. Bob sold 5/6 the remaining pies and Carl sold the rest. Aaron sold 1287
more pies than Carl.
a) How many pies did Bob sell?
b) How many pies did they sell altogether?
Let's start by setting up an equation using the given information. Let's call the total number of pies sold "x".
Aaron sold 5/8 of the total, so he sold (5/8)x pies.
The remaining pies would be 3/8 of the total, so Bob sold 5/6 of 3/8x pies. This can be simplified to (5/6)*(3/8)x = (5/16)x pies.
Carl sold the rest, which would be (1 - 5/8) or 3/8 of the total. Let's call the number of pies Carl sold "c", so c = (3/8)x pies.
We also know that Aaron sold 1287 more pies than Carl, so:
(5/8)x - c = 1287
We can substitute the value of c in terms of x:
(5/8)x - (3/8)x/3 = 1287
Simplifying this equation, we get:
(5/8)x - (1/8)x = 1287
(4/8)x = 1287
x = 2574
So they sold a total of 2574 pies.
Now we can use this value to solve for the other parts of the problem.
a) To find how many pies Bob sold, we need to multiply the remaining pies (5/16 of the total) by the fraction he sold:
(5/16)x * (5/6) = (25/96)x pies
Plugging in x = 2574, we get:
(25/96)*2574 = 668.44 or about 668 pies
So Bob sold about 668 pies.
b) We already know that the total number of pies sold was 2574. Adding up the number of pies each person sold, we get:
Aaron: (5/8)*2574 = 1608 pies
Bob: (25/96)*2574 = 668 pies
Carl: (3/8)*2574 = 1302 pies
Checking to make sure these add up to the total, we have:
1608 + 668 + 1302 = 2578
We're off by 4 pies, but this could be due to rounding errors. Overall, the answer is that they sold a total of 2574 pies.
Let's assume that the total number of pies sold is represented by "x".
a) To find out how many pies Bob sold, we need to determine the remaining pies after Aaron sold his share. Aaron sold 5/8 of the total, leaving 3/8 of the pies. We can represent this as (3/8) * x.
Now, Bob sold 5/6 of the remaining pies, so we can calculate the number of pies Bob sold as (5/6) * (3/8) * x.
Since Aaron sold 1287 more pies than Carl, we can set up an equation: (3/8) * x - x = -1287
Now, let's solve for x.
(3/8) * x - x = -1287
Multiply both sides by 8 to eliminate the fraction:
3x - 8x = -1287 * 8
-5x = -10296
Divide both sides by -5 to solve for x:
x = -10296 / -5
x = 2059.2
Since the number of pies sold must be a whole number, we can conclude that a total of 2059 pies were sold.
b) To find out how many pies they sold altogether, we just need to add up the number of pies sold by each person:
Aaron sold 5/8 * 2059 = 1287 pies
Bob sold (5/6) * (3/8) * 2059 = 771 pies
Carl sold the remaining pies: 2059 - 1287 - 771 = 1 pie
Therefore, they sold a total of 1287 + 771 + 1 = 2059 pies altogether.