Acampus club held a bake sale as a fund raiser, selling coffee, muffins, and bacon and eggs sandwiches. the club members charged $1 for a cup of coffee, 3$ for a muffin , and $4 for a back. and egg sandwich. they sold a total of 55 items , easing $119. of the club members sold 5 more muffins than cups of coffee, how many bacon and egg sandwiches he’s did they sell

The number of  bacon and egg sandwiches sells are 2 .

Step-by-step explanation:

Let us assume that the number of coffee cups campus club sells be x .

Let us assume that the number of muffins  cups campus club sells be y .

Let us assume that the number of bacon and eggs sandwiches campus club sells be z .

As given

Campus club sold a total of 55 items .

Thus the equation becomes

x + y + z = 55

Of the club members sold 5 more muffins than cups of coffee .

Thus

Number of muffins = 5 + Number of cups of coffee

y = 5 + x

Putting the value of y in the equation x + y + z = 55 .

x + 5 + x + z = 55

2x + z = 55- 5

2x + z = 50

As given

The club members charged $1 for a cup of coffee, 3$ for a muffin , and $4 for a bacon and egg sandwich and earns $119 .

Thus the equation becomes

x + 3y + 4z = 119

Putting the value of y in the above

x + 3 × (x + 5) + 4z = 119

x + 3x + 15 + 4z = 119

4x + 4z = 119 - 15

4x + 4z = 104

Simplify the above

x + z = 26

Thus the two equations are

2x + z = 50

x + z = 26

Multiply x + z = 26 subtracted from 2x + z = 50.

2x -x + z - z = 50  - 26

x = 24

Put the value of x in x + z = 26 .

24 + z =26

z = 26 - 24

z = 2

Therefore the number of  bacon and egg sandwiches sells are 2 .