Explanation:
Spending Ratio: 40:4:1.5
Default (GPT-3.5)
User
For each 200 rupees spent by the research department, sales department spends 20 rupees. For every 400 rupees spent by the sales department, the advertising department spends 150 rupees. The ratio of the money spent by the research department to the money spent by the sales department to the money spent by the advertising department can be expressed as:
ChatGPT
Let's denote the money spent by the research department as R, by the sales department as S, and by the advertising department as A.
According to the given information:
Research department spends 200 rupees, so R = 200.
Sales department spends 20 rupees for every 200 rupees spent by the research department, so S = 20 * (R/200) = 20.
Advertising department spends 150 rupees for every 400 rupees spent by the sales department, so A = 150 * (S/400) = 150 * (20/400) = 7.5.
The ratio R:S:A can be expressed as 200:20:7.5, which can be simplified to 40:4:1.5.
User
If x/2 = y/3 = z/4 = (2x - 3y + 5z)/k then the value of
ChatGPT
Let's denote the common ratio as
�
m.
�
2
=
�
3
=
�
4
=
2
�
−
3
�
+
5
�
�
=
�
2
x
=
3
y
=
4
z
=
k
2x−3y+5z
=m
From the first and second fractions:
�
=
�
2
=
�
3
m=
2
x
=
3
y
Cross-multiply to find
�
x and
�
y in terms of
�
m:
�
=
2
�
x=2m
�
=
3
�
y=3m
Now, use these values to find
�
z in terms of
�
m from the third fraction:
�
4
=
�
4
z
=m
�
=
4
�
z=4m
Substitute these values into the fourth fraction:
�
=
2
�
−
3
�
+
5
�
�
m=
k
2x−3y+5z
�
=
2
(
2
�
)
−
3
(
3
�
)
+
5
(
4
�
)
�
m=
k
2(2m)−3(3m)+5(4m)
Simplify and solve for
�
k:
�
=
4
−
9
+
20
�
m=
k
4−9+20
�
=
15
�
m=
k
15
So, the value of
�
m is
15
�
k
15
.
User
Solve it
ChatGPT
Given the relation:
�
2
=
�
3
=
�
4
=
2
�
−
3
�
+
5
�
�
2
x
=
3
y
=
4
z
=
k
2x−3y+5z
We found
�
=
2
�
x=2m,
�
=
3
�
y=3m, and
�
=
4
�
z=4m in terms of the common ratio
�
m.
Now, substitute these into the fourth fraction:
�
=
2
(
2
�
)
−
3
(
3
�
)
+
5
(
4
�
)
�
m=
k
2(2m)−3(3m)+5(4m)
Simplify:
�
=
4
�
−
9
�
+
20
�
�
m=
k
4m−9m+20m
Combine like terms:
�
=
15
�
�
m=
k
15m
Now, solve for
�
k:
�
=
15
�
�
k=
m
15m
�
=
15
k=15
Therefore, the value of
�
k is 15.
User
Write an equation of the line that passes through the given point and is parellel to the given line (5,1), y=-3/5x-3
ChatGPT
The given line has a slope of
−
3
5
−
5
3
. Parallel lines have the same slope. So, the equation of the line parallel to
�
=
−
3
5
�
−
3
y=−
5
3
x−3 and passing through the point
(
5
,
1
)
(5,1) can be written as:
�
−
�
1
=
�
(
�
−
�
1
)
y−y
1
=m(x−x
1
)
Substitute the values
(
�
1
,
�
1
)
=
(
5
,
1
)
(x
1
,y
1
)=(5,1) and
�
=
−
3
5
m=−
5
3
:
�
−
1
=
−
3
5
(
�
−
5
)
y−1=−
5
3
(x−5)
y−1=−
5
3
(x−5)
Distribute the
−
3
5
−
5
3
:
�
−
1
=
−
3
5
�
+
3
y−1=−
5
3
x+3
Now, isolate
�
y by adding 1 to both sides:
�
=
−
3
5
�
+
4
y=−
5
3
x+4
So, the equation of the line parallel to
�
=
−
3
5
�
−
3
y=−
5
3
x−3 and passing through the point
(
5
,
1
)
(5,1) is
�
=
−
3
5
�
+
4
y=−
5
3
x+4.