Two pieces of cake weigh as much as one apple and one cherry. One apple weighs as much as five cherries and one piece of cake. How many cherries weigh as much as one apple?

Question

Two pieces of cake weigh as much as one apple and one cherry. One apple weighs as much as five cherries and one piece of cake. How many cherries weigh as much as one apple?

Answer 1

Let X = cake weight

Let Y = cherry weight
Let Z = apple weight
2X = Y + Z
Z = 5Y + X
Eliminate the variable X to get an equation between Y and Z.
2X = -10Y +2Z (from the second equation, multiplied by two and rearranged)
15Y -Z = 0
Z = 15 Y
15 cherries weight the same as an apple.

Answer 2

Let's assign variables to the quantities mentioned in the problem.

Let:
- Weight of two pieces of cake = C
- Weight of one apple = A
- Weight of one cherry = X

Based on the given information:
1) Two pieces of cake weigh as much as one apple and one cherry:
2C = A + X (Equation 1)

2) One apple weighs as much as five cherries and one piece of cake:
A = 5X + C (Equation 2)

To find the weight of cherries that is equivalent to one apple, we can solve these equations.

From Equation 2, we can express C in terms of A and X by rearranging the equation:
C = A - 5X (Equation 3)

Substituting Equation 3 into Equation 1, we can solve for X:
2(A - 5X) = A + X

Expanding the equation:
2A - 10X = A + X

Combining like terms:
A = 11X

Therefore, one apple weighs as much as eleven cherries.

To answer the question, one apple weighs as much as eleven cherries.

Answer 3

To solve this problem, let's assign some variables to the given information. Let's say the weight of one piece of cake is represented by 'C', the weight of one apple is represented by 'A', and the weight of one cherry is represented by 'H'.

From the first statement, we can write the equation:
2C = A + H ----- (Equation 1)

From the second statement, we have:
A = 5H + C ----- (Equation 2)

Now, we can substitute the value of A from Equation 2 into Equation 1, like this:
2C = (5H + C) + H

Simplifying this equation, we get:
2C = 6H + C

Subtracting C from both sides, we have:
C = 6H

So, one piece of cake weighs as much as six cherries.

Now, we need to find the number of cherries that weigh the same as one apple.

We know that A = 5H from Equation 2.

Substituting 5H for A, we get:
5H = 6H

Now, we can solve for the value of H:
5H - 6H = 0
-H = 0
H = 0

Therefore, no cherries weigh the same as one apple, based on the given information.

Please note that if there is any additional information or if the given information is incomplete, the answer may change.