Kim's coffee shop sells a cup of tea for $1.05, a cup of coffee for $1.35, and a cup of hot chocolate for $2.25 . One busy day, 20 more cups of coffee than of hot chocolate were sold, and 30 more cups of coffee than tea, for a total of 202.50 for all three hot drinks. How many cups of each drink were sold?

Question

amistre64 · Answer

hmmm..... lets see

amistre64 · Answer

t is the standard for measuing the rest:

c = t+30

h = t+30+20 = t+50

amistre64 · Answer

amount times cost = total

t(1.05) + (t+30)(1.35) + (t+50)(2.25) = 202.50

amistre64 · Answer

multiply by 100 to get rid of decimals

105t +135t +135(30) + 225t +225(50) = 20250

amistre64 · Answer

465t = 20250 - 135(30) - 225(50)

amistre64 · Answer

$$t = \frac{20250 - 135(30) - 225(50)}{465}$$t

amistre64 · Answer

t=10.64 cups sold  lol

c = 40.64

h = 60.64  if i did it right

anonymous · Answer

I think I understand it , but I see where you went wrong because t+ 50 should've actually been t+ 10 . but thanks anyways ! it helped ! :)

amistre64 · Answer

10 40 and 60 gets you 199.50 total so its good

amistre64 · Answer

ahhh...youre right :)  my stupidy got me again lol

anonymous · Answer

lol , don't say that ! you figured it out even with the error ! :)

amistre64 · Answer

hahaha   fools luck i spose :)

anonymous · Answer

lol, yeah

amistre64 · Answer

105t +135t +135(30) + 225t +225(10) = 20250

465t = 20250 - 4050 - 2250

t = 13950/465

t = 30
c = 60
h = 40 are my new numbers :)

30(1.05) + 60(1.35) + 40(2.25) = 202.50

31.50 + 81.00 + 90.00 = 202.50

31.50 + 171.00 = 202.50

202.50 = 202.50....checks ;)

anonymous · Answer

thank you soo much ! :) you're very smartt