c. Answer the following questions in about 30 words each.
1. How did the woman know the narrator? Why did she want to meet him?
2. What impression did the narrator gather of the woman when he met her?
4. Why did the narrator order coffee for himself also?
walter carry a basket full of
2. Why was the narrator pante-stricken while they were waiting for the asparagus
to be cooked?
3. What is the waiter's contribution in allowing the woman to have a gorgeous meal?
Answers
Question:
Solve the given equation:
\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}
4
3
−2x
3
x
−
5
2
=
15
16
Answer:
The value of x is
\displaystyle{\implies\boxed{\red{\sf\:x\:=\:\dfrac{18}{37}}}}⟹
x=
37
18
Step-by-step-explanation:
The given equation is \displaystyle\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}
4
3
−2x
3
x
−
5
2
=
15
16
.
Now,
\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}
4
3
−2x
3
x
−
5
2
=
15
16
\displaystyle{\implies\sf\:\dfrac{\dfrac{5x\:-\:6}{15}}{\dfrac{3\:-\:8x}{4}}\:=\:\dfrac{16}{15}}⟹
4
3−8x
15
5x−6
=
15
16
\displaystyle{\implies\sf\:\dfrac{5x\:-\:6}{15}\:\times\:\dfrac{4}{3\:-\:8x}\:=\:\dfrac{16}{15}}⟹
15
5x−6
×
3−8x
4
=
15
16
\displaystyle{\implies\sf\:\dfrac{4\:\times\:(\:5x\:-\:6\:)}{15\:\times\:(\:3\:-\:8x\:)}\:=\:\dfrac{16}{15}}⟹
15×(3−8x)
4×(5x−6)
=
15
16
\displaystyle{\implies\sf\:\dfrac{20x\:-\:24}{45\:-\:120x}\:=\:\dfrac{16}{15}}⟹
45−120x
20x−24
=
15
16
\displaystyle{\implies\sf\:15\:\times\:(\:20x\:-\:24\:)\:=\:16\:\times\:(\:45\:-\:120x\:)}⟹15×(20x−24)=16×(45−120x)
\displaystyle{\implies\sf\:300x\:-\:360\:=\:720\:-\:1920x}⟹300x−360=720−1920x
\displaystyle{\implies\sf\:300x\:+\:1920x\:=\:720\:+\:360}⟹300x+1920x=720+360
\displaystyle{\implies\sf\:2220x\:=\:1080}⟹2220x=1080
\displaystyle{\implies\sf\:x\:=\:{\dfrac{108\cancel{0}}{222\cancel{0}}}}⟹x=
222
0
108
0
\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{108}{222}}}⟹x=
222
108
\displaystyle{\implies\boxed{\red{\sf\:x\:=\:\dfrac{18}{37}}}}⟹
x=
37
18
─────────────────────
Verification:
The given equation is
\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}
4
3
−2x
3
x
−
5
2
=
15
16
The value of x is \displaystyle\sf\:\dfrac{18}{37}
37
18
By substituting this value of x in the LHS of the given equation, we get,
\displaystyle\sf\:LHS\:=\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}LHS=
4
3
−2x
3
x
−
5
2
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{\dfrac{18}{37}}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2\:\times\:\dfrac{18}{37}}}⟹LHS=
4
3
−2×
37
18
3
37
18
−
5
2
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{\cancel{18}}{37}\:\times\:\dfrac{1}{\cancel{3}}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:\dfrac{39}{37}}}⟹LHS=
4
3
−
37
39
37
18
×
3
1
−
5
2
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{6}{37}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:\dfrac{36}{37}}}⟹LHS=
4
3
−
37
36
37
6
−
5
2
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{6\:\times\:5\:-\:2\:\times\:37}{37\:\times\:5}}{\dfrac{3\:\times\:37\:-\:36\:\times\:4}{4\:\times\:37}}}⟹LHS=
4×37
3×37−36×4
37×5
6×5−2×37
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{30\:-\:74}{185}}{\dfrac{111\:-\:144}{148}}}⟹LHS=
148
111−144
185
30−74
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{-\:44}{185}}{\dfrac{-\:33}{148}}}⟹LHS=
148
−33
185
−44
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\cancel{-}\:44}{185}\:\times\:\dfrac{148}{\cancel{-}\:33}}⟹LHS=
185
−
44
×
−
33
148
\displaystyle{\implies\sf\:LHS\:=\:\cancel{\dfrac{\cancel{44}}{185}}\:\times\:\dfrac{148}{\cancel{33}}}⟹LHS=
185
44
×
33
148
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{4}{185}\:\times\:\dfrac{148}{3}}⟹LHS=
185
4
×
3
148
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{4\:\times\:148}{185\:\times\:3}}⟹LHS=
185×3
4×148
\displaystyle{\implies\sf\:LHS\:=\:\cancel{\dfrac{592}{555}}}⟹LHS=
555
592
\displaystyle{\implies\sf\:LHS\:=\:\dfrac{16}{15}}⟹LHS=
15
16
\displaystyle{\implies\sf\:RHS\:=\:\dfrac{16}{15}}⟹RHS=
15
16
\displaystyle{\implies\boxed{\red{\sf\:LHS\:=\:RHS}}}⟹
LHS=RHS
Hence verified!