Respuesta :
Answer:
The number of red marbles is 46.
Step-by-step explanation:
Given that, there are some marbles in a box. [tex]\frac14[/tex] of them are red.
Assume x be the number of marbles in the box.
The number of red marble is [tex]=\frac{1}{4}\times x[/tex]
[tex]=\frac{x}{4}[/tex]
The remainder marbles are [tex]=x-\frac x 4[/tex]
[tex]=\frac{4x-x}{4}[/tex]
[tex]=\frac{3x}{4}[/tex]
[tex]\frac16[/tex] of the remainder marbles are blue.
The number of blue marbles are [tex]=\frac{3x}{4}\times \frac{1}6[/tex]
[tex]=\frac x8[/tex]
The remainder marbles are [tex]=\frac{3x}{4}-\frac x8[/tex]
[tex]=\frac{6x-x}{8}[/tex]
[tex]=\frac{5x}{8}[/tex]
According to the problem,
[tex]\frac{5x}{8}=115[/tex]
[tex]\Rightarrow x=\frac{115\times 8}{5}[/tex]
[tex]\Rightarrow x=184[/tex]
The number of red marbles is [tex]=\frac{x}{4}[/tex]
[tex]=\frac{184}{4}[/tex]
=46
