You have 100 pieces of candy in five bowls. The sum of candy in bowl a and bowl b is 30 pieces. The sum of candy in bowl b and c is 36 pieces. The sum of candy in bowl c and bowl d is 49 pieces of candy. The sum of bowl d and bowl e is 47 pieces of candy. How many pieces of candy are in each bowl?
a + b + c + d + e = 100
a + b = 30
b + c = 36
c + d = 49
d + e = 47
a = 30 - b
c = 36 - b
d = 49 - c = 49 - (36 - b) = 13 + b
e = 47 - d = 47 - (49 - c) = c - 2 = (36 - b) - 2 = 34 - b
(30 - b) + b + (36 - b) + (13 + b) + (34 - b) = 100
113 - b = 100
b = 13
Therefore,
Bowl A = 30 - 13 = 17
Bowl B = 13
Bowl C = 36 - 13 = 23
Bowl D = 13 + 13 = 26
Bowl E = 34 - 13 = 21
To solve this problem, we need to set up a system of equations based on the information provided.
Let's assign variables to the number of candies in each bowl:
Let a represent the number of candies in bowl A.
Let b represent the number of candies in bowl B.
Let c represent the number of candies in bowl C.
Let d represent the number of candies in bowl D.
Let e represent the number of candies in bowl E.
Based on the given information, we can write the following equations:
1. a + b = 30
2. b + c = 36
3. c + d = 49
4. d + e = 47
Now, we can solve these equations to find the values of a, b, c, d, and e.
From equation 1, we can express a in terms of b: a = 30 - b.
From equation 2, we can express c in terms of b: c = 36 - b.
From equation 3, we can express d in terms of c: d = 49 - c.
Substituting these expressions into equation 4, we get:
(49 - c) + e = 47
49 - c + e = 47
Rearranging this equation, we have e = c - 2.
Now, we have expressions for a, b, c, d, and e in terms of b and c. We can substitute these back into the previous equations to solve for the values.
Using equation 1:
a + b = 30
(30 - b) + b = 30
30 - b + b = 30
30 = 30
This equation is true, which means any value of b will satisfy it. Since we have 100 pieces of candy and need to split them among the five bowls, let's assume each bowl has an equal number of candies. So, b = 100/5 = 20.
Now, substituting b = 20 into the other equations:
a + 20 = 30 -> a = 10
20 + c = 36 -> c = 16
16 + d = 49 -> d = 33
33 + e = 47 -> e = 14
So, the number of pieces of candy in each bowl is:
Bowl A: 10 pieces
Bowl B: 20 pieces
Bowl C: 16 pieces
Bowl D: 33 pieces
Bowl E: 14 pieces