SOLUTION: constructing equations how do you construct this into a equatin? a spa had specials for new members. they can get 3 facials and 5 manicures for $114 or 3 facials and 2 manicure

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Question 262410: constructing equations
how do you construct this into a equatin?
a spa had specials for new members. they can get 3 facials and 5 manicures for $114 or 3 facials and 2 manicures for $78. what are the prices for facials and manicures?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.