Question 1203641
g = number of guppies
f = number of goldfish
g = f + 35


g + 1/6 * g + f + 3/5 * f = 193
simplify to get:
7/6 * g + 8/5 * f = 193


you are given that g = f + 35
replace g in the equation of 7/6 * g + 8/5 * f = 193 with f + 35 to get:
7/6 * (f + 35) + 8/5 * f = 193
simplify to get:
7/6 * f + 7/6 * 35 + 8/5 * f = 193


multiply both sides of the equation by 30 to get:
35 * f + 35 * 35 + 48 * f = 193 * 30
simplify to get:
35 * f + 1225 + 48 * f = 5790


combine like terms to get:
83 * f + 1225 = 5790
subtract 1225 from both sides of the equation to get:
83 * f = 4565
solve for f to get:
f = 55


since g = f + 35, then you get:
f = 55
g = 90


confirm by replacing g and f in the original equations to get:


g = f + 35 becomes 90 = 55 + 35 which becomes 90 = 90.
this confirmns that g = f + 35 is true.


g + 1/6 * g + f + 3/5 * f = 193 becomes:
90 + 1/6 * 90 + 55 + 3/5 * 55 = 193 which becomes:
105 + 88 = 193 which becomes 193 = 193.
this confirms that g + 1/6 * g + f + 3/5 * f is true.


your solution is that there were 105 guppies in the end.
that would be 90 guppies to start plus 1/6 * 90 = 15 guppies for a total of 105 guppies in the end.