PLEASE I NEED HELP......
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?
first let's represent their weights using variables:
let C = weight of one piece of cake
let A = weight of one apple
let H = weight of one cherry
from the first statement,
(1) 2C = A + H
for the second statement,
(2) A = 5H + C
now we need to find how mach does cherries weigh as much as 1 apple. thus we need to manipulate these equations so that the weight of cake, C will not be involved in the final equation (in other words, we'll eliminate C)
first, from equation (2), we transpose C to the left side and A to the right side, and multiply both sides by 2, and it becomes:
-2C = -2A + 10H
then we add this to equation (1):
2C = A + H
-2C = -2A + 10H
---------------------
0 = -A + 11H
A = 11H
therefore, 1 apple weighs as much as 11 cherries.
hope this helps~ :)
Well, it seems like we have a fruity cake situation here. Let's break it down.
We have two pieces of cake that weigh the same as one apple and one cherry. Now, if we convert everything into cherries for simplicity, we can say that one piece of cake is equal to five cherries.
Since one apple weighs as much as five cherries and one piece of cake, it means that one apple weighs the same as one piece of cake, which is equal to five cherries.
Therefore, we can conclude that one apple weighs the same as five cherries.
To solve this problem, let's assign variables to the weights of the cake, apple, and cherry.
Let's denote the weight of the cake as C, the weight of the apple as A, and the weight of the cherry as X.
From the given information:
1. "Two pieces of cake weigh as much as one apple and one cherry": 2C = A + X
2. "One apple weighs as much as five cherries and one piece of cake": A = 5X + C
We can use these equations to solve for the number of cherries that weigh as much as one apple.
First, let's substitute equation 2 into equation 1 to eliminate A:
2C = (5X + C) + X
2C = 6X + C
Next, let's simplify the equation:
C = 6X
Now, let's substitute C = 6X back into equation 2:
A = 5X + 6X
A = 11X
Therefore, one apple weighs as much as 11 cherries.
To find the number of cherries that weigh as much as one apple, we divide the weight of the apple by the weight of one cherry:
11 cherries / 1 apple = 11 cherries
So, the answer is that 11 cherries weigh as much as one apple.
To solve this problem, we need to assign variables to each item mentioned. Let's say:
C = weight of one cherry
A = weight of one apple
P = weight of one piece of cake
According to the given information:
1) "Two pieces of cake weigh as much as one apple and one cherry."
This can be written as: 2P = A + C
2) "One apple weighs as much as five cherries and one piece of cake."
This can be written as: A = 5C + P
Now, we can solve these two equations simultaneously to find the value of C:
Substitute the value of A from the second equation into the first equation:
2P = (5C + P) + C
Combine like terms:
2P = 6C + P
Subtract P from both sides of the equation:
2P - P = 6C + P - P
P = 6C
So, one apple weighs the same as six cherries.