Answer:
There are 55 sweets in total.
Step-by-step explanation:
The total number of sweets is t.
Henry, Brian and Colin share some sweets in the ratio 6:4:1.
This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).
Brian earns [tex]\frac{4}{11}[/tex] of the total.
Colin earns [tex]\frac{1}{11}[/tex] of the total
Henry gets 25 more sweets than Colin.
Henry earns [tex]\frac{6t}{11}[/tex]
Colin earns [tex]\frac{t}{11}[/tex]
So
[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]
Multiplying everything by 1
[tex]6t = t + 275[/tex]
[tex]5t = 275[/tex]
[tex]t = \frac{275}{5}[/tex]
[tex]t = 55[/tex]
There are 55 sweets in total.
