please solve

Question

A busload of campers stopped at a dairy stand for ice cream. They ordered 75 cones, some soft served at $2.00 each and the rest hard packed at $0.75 each. If the total bill was 101.25, how  many of each type of cone were ordered?

 

How many soft serve cones?

 

How many hard packed cones?

Answer 1

Let S = # soft serve cones

Let H = # hard packed cones

 

S + H = 75 since they bought 75 total cones

 

For the dollar amount we have 2S + .75H = 101.25 since each soft cone is $2 and each hard cone is $.75

and the total dollars spent was $101.25

 

We have two simultaneous equations:

 

  S +     H = 75

2S + .75H = 101.25

 

Let's solve by elimination... multiply the top equation through by -2 giving

 

-2S - 2H = -150

 2S + .75H = 101.25

 

Now add straight down giving:

 

-1.25H = -48.75

H = (-48.75)/(-1.5) = 39

 

Thus they bought 39 hard packed cones.

The # soft cones is 75 - H = 36 soft cones