## anonymous 5 years ago 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?

1. amistre64

hmmm..... lets see

2. amistre64

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

3. amistre64

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

4. amistre64

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

5. amistre64

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

6. amistre64

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

7. amistre64

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

8. anonymous

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 ! :)

9. amistre64

10 40 and 60 gets you 199.50 total so its good

10. amistre64

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

11. anonymous

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

12. amistre64

hahaha fools luck i spose :)

13. anonymous

lol, yeah

14. amistre64

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 ;)

15. anonymous

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