Explanation:
Let
�
R be the number of red marbles and
�
B be the number of blue marbles.
Given the ratio of red marbles to blue marbles is 1:6.
This implies that the total number of parts in the ratio is
1
+
6
=
7
1+6=7 (1 part for red, 6 parts for blue).
The total number of marbles is 105.
Let's set up the equation:
Since the total parts in the ratio is 7 and the total number of marbles is 105:
Each part of the ratio represents
105
7
=
15
7
105
=15 marbles.
For red marbles, there is 1 part representing them, so
�
=
1
×
15
=
15
R=1×15=15 red marbles.
For blue marbles, there are 6 parts representing them, so
�
=
6
×
15
=
90
B=6×15=90 blue marbles.
Therefore, there are 15 red marbles in the bag.