Answer:
Let's denote the number of blue chairs as
�
B and the number of yellow chairs as
�
Y.
The ratio of blue chairs to yellow chairs is given as 1 to 4, which can be expressed as:
�
�
=
1
4
Y
B
=
4
1
We also know that the total number of chairs in the room is 50:
�
+
�
=
50
B+Y=50
Now, let's use the information to solve for
�
B and
�
Y.
From the ratio, we can express
�
B in terms of
�
Y:
�
=
1
4
�
B=
4
1
Y
Now, substitute this expression for
�
B into the equation for the total number of chairs:
1
4
�
+
�
=
50
4
1
Y+Y=50
Combine the terms:
5
4
�
=
50
4
5
Y=50
Now, solve for
�
Y:
�
=
4
5
×
50
=
40
Y=
5
4
×50=40
Now that we know
�
=
40
Y=40, we can find
�
B using the equation
�
+
�
=
50
B+Y=50:
�
+
40
=
50
⟹
�
=
10
B+40=50⟹B=10
Finally, to find how many more yellow chairs there are than blue chairs:
Yellow chairs
−
Blue chairs
=
40
−
10
=
30
Yellow chairs−Blue chairs=40−10=30
So, there are 30 more yellow chairs than blue chairs.