Question

PART A :A deli receives a large order for sandwiches for a company picnic. The company wants one club sandwich and two regular sandwiches for each person. The company also wants an extra Dagwood sandwich. A club sandwich has $3$ slices of bread. A regular sandwich has $2$ slices. A Dagwood has $5$ slices. If there are $n$ people going to the company picnic, how many slices of bread does the deli need to make this order? Write your answer as a fully simplified expression. Your answer should have the variable $n$ in it exactly once. PART B: Given that the deli ends up using $110$ slices of bread, how many people are going to the company picnic?

Answer 1

Part A:

`7n + 5`

Part B:

15 people

Explanation:

Each person gets one club sandwich and two regular sandwiches. There is one additional Dagwood sandwich.

If a club sandwich has 3 slices, then the total amount of slices needed for
`n` people will be
`3n`, since each person has 3 slices.

If a regular sandwich has 2 slices and everybody gets 2 regular sandwiches, then it's represented as
`4n`, since everyone has 4 slices each.

Additionally, we have one Dagwood sandwich, which can be represented as 5,, since a Dagwood sandwich has 5 slices.

Combining these terms we get
`3n + 4n + 5`. Combining like terms gets us the expression
`7n + 5`.

To solve for
`7n + 5`, we have to make it an equation. Using the information in Part B, the Deli ends up receiving 110 slices of bread. So, the equation is

`7n + 5=110`

We want to isolate n on one side, to do this we have to subtract 5 then divide by 7.

`7n + 5 - 5= 110-5\\\\7n = 105\\\\7n/7 = 105/7\\\\n = 15`

So 15 people are going to the picnic.

Hope this helped!