Question

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ρℓєαѕє αиѕωєя тнє тωσ qυєѕтισиѕ ιи тнє ρι¢тυяє..тнє fιяѕт αиѕωєя ιѕ 252 км αи∂ ѕє¢σи∂ ιѕ $12.35. иσ ѕραм❌❌❌​

Answer 1

$\underline{\underline{\bold{Question:1.}}}$

A bus travels at 36 km h⁻¹ and arrives at its destination half an hour late . If it travels at 42 km h⁻¹ , it arrives at the destination half an hour earlier . Find the journey's distance .

$\mathfrak{Answer:}$

= 252 km.

$\mathfrak{Step-By-Step\;Explanation:}$

Let the journey's distance be x km.

$\boxed{\bold{Time=\dfrac{Distance}{Speed}.}}$

In 1st Case:

• Speed = 36 km h⁻¹.

$\bold{Time=\dfrac{x\;km}{36\;km\;h^{-1}}}\\\\\\\tt{=\dfrac{x}{36}\;hrs.}$

In 2nd Case:

• Speed = 42 km h⁻¹.

$\bold{Time=\dfrac{x\;km}{42\;km\;h^{-1}}}\\\\\\\tt{=\dfrac{x}{42}\;hrs.}$

$\mathfrak{According\:to\:Question:}$

$\implies\tt{\dfrac{x}{36}-\dfrac{30}{60}=\dfrac{x}{42}+\dfrac{30}{60}}\\\\\\\implies\tt{\dfrac{x}{36}-\dfrac{x}{42}=\dfrac{1}{2}+\dfrac{1}{2}}\\\\\\\implies\tt{=\dfrac{7x-6x}{252}=\dfrac{1+1}{2}}\\\\\\\implies\tt{\dfrac{x}{252}=\dfrac{2}{2}}\\\\\\\implies\tt{\dfrac{x}{252}=1}\\\\\\\therefore\quad\tt{x=252.}$

$\boxed{\boxed{\bold{Journey's\;distance=252\;km.}}}$

$\underline{\underline{\bold{Question:2.}}}$

Mrs. Lim buys 30 kg cheese at a certain price .She finds that if she had bought some cheaper cheese costing 95 cents less per kg . She could have had 32 1/2 kg for the same amount of money. What is the price per kg of the cheese which is more expensive ?

$\mathfrak{Answer:}$

= $ 12.35 .

$\mathfrak{Step-By-Step\;Explanation:}$

Let the price per kg of the cheese which is more expensive be x cents per kg.

• Amount = 30 kg.

So total cost = 30 × x = 30 x cents.

Now the price of cheaper cheese per kg = (x - 95) cents per kg.

• Amount = 32.5 kg.

So total cost = 32.5 (x - 95) cents.

$\mathfrak{According\;to\;Question:}$

$\implies\tt{30x=32.5(x-95)}\\\\\\\implies\tt{30x=32.5x-3087.5}\\\\\\\implies\tt{32.5x-30x=3087.5}\\\\\\\implies\tt{2.5x=3087.5}\\\\\\\implies\tt{x=\dfrac{3087.5}{2.5}}\\\\\\\therefore\quad\tt{x=1235.}$

$\boxed{\bold{1\ =100\;cents.}}$

$\boxed{\boxed{\bold{Rate\;of\;Cheese=1235\;cents\;per\;kg=\ 12.35\;per\;kg.}}}$

Answer 2

I have been give both answers in attachment:

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