Question 262410
let f equal the cost for a facial.
let m = the cost for a manicure.


first equation is:


3*f + 5*m = 114


second equation is:


3*f + 2*m = 78


you need to solve these 2 equations simultaneously.


we will solve by elimination.


the two equations are:


3*f + 5*m = 114
3*f + 2*m = 78


subtract second equation from first equation to get:


3*m = 36


solve for m to get:


m = 12


substitute in first equation to get:


3*f + 5*12 = 114


solve for f to get:


f = 54/3 = 18


you have:


m = 12
f = 18


substitute in first equation to get:


3*f + 5*m = 114 becomes 3*18 + 5*12 = 54 + 60 = 114


substitute in second equation to get:


3*f + 2*m = 78 becomes 3*18 + 2*12 = 54 + 24 = 78


both original equations are true confirming the values for m and f are good.


your answer is:


cost of a facial is 18 dollars.
cost of a manicure is 12 dollars.