Answer: the number of adults is 136
At a firefighters pancake breakfast, the fire fighters raised $1,273.00 by serving 276 people
This implies that he served both children and adult and theie number sum up to 276
Let the number of adults be x
Let the number of children be y
Mathematically,
x + y = 276 -------- equation 1
The cost of an adult ticket is $5.50 and the cost a child's ticket for the breakfast is $3.75
The total money he realized from both the adults and children taking the breakfast is $1,273
Mathematically, the equation can be written as
5.5 * x + 3.75 x y = 1273
5.5x + 3.75y = 1273 ------------ equation 2
The two systems of equation can be solve simultaneously
x + y = 276 ---------------------- 1
5.5x + 3.75y = 1273 -------------- 2
Make y the subject of the formula in equation 1
y = 276 - x ------------ 3
Substitute equation 3 into equation 2
5.5x + 3.75(276 - x ) = 1273
Open the parenthesis
5.5x + 3.75 x 276 - 3.75 * x = 1273
5.5x + 1035 - 3.75x = 1273
Collect the like terms
5.5x - 3.75x = 1273 - 1035
1.75x = 238
Divide both sides by 1.75
x = 238 / 1.75
x = 136
Hence, the number of adults is 136