Find the amount of Small, Medium and Large cups sold

Question

A drinks stall sells small, medium and large cups of fruit drink for $1.50, $2 and @2.50 respectively. In one morning three times as many medium cups were sold as small cups, and the number of large cups sold was 140 less than the number of medium cups. If the total of the drinks sales was $1360, how many of each size cup were sold?

Answer 1

Hi Hester

 

S = # small cups @ $1.50 each

M = # medium cups @ $2 each

L = # large cups @ $2.50 each

 

M = 3S  and S = M/3

L = M - 140

 

1.5S + 2M + 2.5L = 1360

Using substitution

1.5(M/3) + 2M + 2.5(M-140) = 1360

M/2 + 2M + 2.5M - 350 = 1360

5M - 350 = 1360

5M = 1710

M = 342

 

If M = 342, 

L = 342 - 140 = 202

S = M/3 = 342/3 = 114

 

There were 

114 small cups

342 medium cups

and

202 large cups sold.