Question 1200889
<font color=black size=3>
Answers: 
(a) <font color=red>2000</font>
(b) <font color=red>200</font>



Work Shown:


3/5 were chicken buns.
The rest (2/5) were tuna buns.


c = number of chicken buns
t = number of tuna buns
c+t = number of total buns
(3/5)*(total) = number of chicken buns
(3/5)*(c+t) = number of chicken buns
(3/5)*(c+t) = c
3(c+t) = 5c
3c+3t = 5c
3t = 5c-3c
3t = 2c
c = 3t/2
c = 1.5t
This will be used later in a <font color=blue>substitution step</font>


7/8 of the chicken buns and 600 of the tuna buns were eaten
7/40 of all the buns were left. Therefore, 33/40 of the buns were eaten

(7/8)c = number of chicken buns eaten
600 = number of tuna buns eaten
(7/8)c + 600 = number of buns eaten
(7/8)c + 600 = (33/40)*(total number of buns)
(7/8)c + 600 = (33/40)*(c+t) 
(7/8)*1.5t + 600 = (33/40)*(1.5t+t) ........... <font color=blue>substitution step</font>
(21/16)t + 600 = (33/16)t
16*((21/16)t + 600) = 16*(33/16)t
21t + 9600 = 33t
9600 = 33t-21t
9600 = 12t
t = 9600/12
t = 800 tuna buns to start with
600 were eaten, so 800-600 = <font color=red>200 tuna buns remain.</font>


c = 1.5t
c = 1.5*800
c = 1200 chicken buns to start with
c+t = 1200+800 = <font color=red>2000 total buns to start with</font>



Check:
3/5 of 2000 = (3/5)*2000 = 1200 chicken buns to start
2/5 of 2000 = (2/5)*2000 = 800 tuna buns to start
7/8 of 1200 chicken buns = (7/8)*1200 = 1050 chicken buns eaten. Add on the 600 tuna buns eaten to get 1050+600 = 1650 total eaten.
2000-1650 = 350 buns remain
350/2000 = 7/40 of the original buns remain
This confirms the answers.


Another way to check:
<table border = "1" cellpadding = "5"><tr><td></td><td>Chicken</td><td>Tuna</td><td>Total</td></tr><tr><td>Start</td><td>1200</td><td>800</td><td><font color=red>2000</font></td></tr><tr><td>Eaten</td><td>(7/8)*1200 = 1050</td><td>600</td><td>1050+600 = 1650</td></tr><tr><td>End</td><td>1200-1050 = 150</td><td>800-600 = <font color=red>200</font></td><td>150+200 = 350 (or 2000-1650 = 350)</td></tr></table>
The table mentions:
350 total buns remaining out of 2000 starting buns.
350/2000 = 7/40 of the original buns remain
</font>