Mary’s mother made 102 chicken sandwiches and tuna sandwiches
for Mary’s birthday party. After her friends had eaten _5
8 of the chicken
sandwiches and _23 of the tuna sandwiches, an equal number of chicken
and tuna sandwiches were left. How many sandwiches of each type
did Mary’s mother make?
Let's solve the problem step by step:
Step 1: Let's assume the total number of sandwiches Mary's mother made is x.
- We can assume that Mary's mother made x chicken sandwiches.
- So, the number of tuna sandwiches made is also x.
- Therefore, the total number of sandwiches made is 2x.
Step 2: After her friends had eaten 58 chicken sandwiches and 23 tuna sandwiches, an equal number of chicken and tuna sandwiches were left.
- The number of chicken sandwiches left is x - 58.
- The number of tuna sandwiches left is x - 23.
Step 3: The number of chicken sandwiches left is equal to the number of tuna sandwiches left.
- So, x - 58 = x - 23.
- Simplifying the equation, we get:
x - x = 23 - 58
0 = -35
Step 4: Since we got a contradictory equation, it means our assumption in step 1 was incorrect.
- This means that there is no possible solution to the problem.
Conclusion: Mary's mother did not make a possible number of sandwiches for the given scenario.
To solve this problem, let's break it down step by step:
Step 1: Write down the given information
- Mary's mother made a total of 102 sandwiches.
- Mary's friends ate 58 of the chicken sandwiches.
- Mary's friends ate 23 of the tuna sandwiches.
- An equal number of chicken and tuna sandwiches were left.
Let's assume the number of chicken and tuna sandwiches left is represented by 'x'.
Step 2: Form equations based on the given information
- The total number of chicken sandwiches is 102 - 58 = 44.
- The total number of tuna sandwiches is 102 - 23 = 79.
- Since an equal number of chicken and tuna sandwiches were left, we can write the equation: x = x.
Step 3: Solve the equations
From the previous step, we have two equations:
1) 44 - x = x (equation for chicken sandwiches)
2) 79 - x = x (equation for tuna sandwiches)
Let's solve equation (1):
44 - x = x
44 = 2x
Divide both sides by 2
22 = x
Now, substitute the value of x (22) into equation (2):
79 - x = x
79 - 22 = 22
57 = x
So, Mary's mother made 22 chicken sandwiches and 57 tuna sandwiches.
c+t = 102
3/8 c = 1/3 t
Now just solve for c and t