A group of friends decided to eat sandwiches. Their team leaders, Franco, Clint and Valir bought 46 sandwiches altogether for their organization’s getaway. Franco bought 5 more sandwiches than Valir. Meanwhile, Valir bought 8 less sandwiches than Clint. How many sandwiches did each team leader buy?
F + C + V = 46
F = V + 5
C = V + 8
(V + 5) + (V + 8) + V = 46 ... 3 V + 13 = 46
65
To solve this problem, let's assign variables for the number of sandwiches each team leader bought. Let's say:
- The number of sandwiches Franco bought is F.
- The number of sandwiches Clint bought is C.
- The number of sandwiches Valir bought is V.
We have three pieces of information from the problem statement:
1) Franco bought 5 more sandwiches than Valir: F = V + 5.
2) Valir bought 8 less sandwiches than Clint: V = C - 8.
3) The total number of sandwiches bought is 46: F + C + V = 46.
Now, we can solve this system of equations to find the values of F, C, and V.
Using the first equation, substitute F from equation 1 into equation 3:
(V + 5) + C + V = 46
2V + C + 5 = 46
Next, substitute V from equation 2 into the new equation:
2(C - 8) + C + 5 = 46
2C - 16 + C + 5 = 46
3C - 11 = 46
Now, solve for C:
3C = 46 + 11
3C = 57
C = 57 / 3
C = 19
Substitute the value of C back into equation 2 to find V:
V = 19 - 8
V = 11
Finally, substitute the values of V and C into equation 1 to find F:
F = 11 + 5
F = 16
Therefore, Franco bought 16 sandwiches, Clint bought 19 sandwiches, and Valir bought 11 sandwiches.