Answer:
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 .
