He will need 315 sandwiches to make each day next week
Step-by-step explanation:
The given:
- Friday's meeting needs 12 more sandwiches than Tuesday
- Tuesday needs 6 fewer than Monday
- Monday needs 20 more than Wednesday
- Wednesday needs 5 fewer than Thursday
- The number of sandwiches ordered for the meeting that calls for the fewest is 50
We need to find how many sandwiches he will need to make each day next week
Assume that Tuesday needs x sandwiches
∵ Friday's meeting needs 12 more sandwiches than Tuesday
∵ Tuesday needs x sandwiches
- Add x by 12 to find Friday's need
∴ Friday needs = x + 12
∵ Tuesday needs 6 fewer than Monday
- That means Monday needs 6 more than Tuesday, add 6 to x
to find Monday needs
∴ Monday needs = x + 6
∵ Monday needs 20 more than Wednesday
- That means Wednesday needs 20 less than Monday, subtract
20 from Monday needs to find Wednesday needs
∴ Wednesday needs = x + 6 - 20 = x - 14
∵ Wednesday needs 5 fewer than Thursday
- That means Thursday needs 5 more than Wednesday, add 5 to
Wednesday needs to find Thursday needs
∴ Thursday needs = x - 14 + 5 = x - 9
∵ The number of sandwiches ordered for the meeting that calls
for the fewest is 50
- From the days needs above the fewest one is Wednesday, then
equate Wednesday needs by 50
∵ Wednesday needs is x - 14
∴ x - 14 = 50
- Add 14 to both sides
∴ x = 64
Substitute x in each day needs to find the number of sandwiches
∵ Tuesday needs is x
∴ Tuesday needs = 64
∵ Friday needs is x + 12
∴ Friday needs = 64 + 12 = 76
∵ Monday needs is x + 6
∴ Monday needs = 64 + 6 = 70
∵ Wednesday needs = 50
∵ Thursday needs is x - 9
∴ Thursday needs = 64 - 9 = 55
Add the numbers of sandwiches of all day to find the number of sandwiches he will need to make each day next week
∵ The number of sandwiches = 76 + 64 + 70 + 50 + 55
∴ The number of sandwiches = 315
He will need 315 sandwiches to make each day next week
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