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n200080 [17]
3 years ago
14

How much salt should Ilya add to 810g of water to make 10% solution? How much solution will he make? Ilya should add __g of salt

and he will make __g of solution
Mathematics
1 answer:
Burka [1]3 years ago
5 0

Answer:

90 g of water should be added and he will make 900 g of solution.

Step-by-step explanation:

Let x g be the amount of salt Ilya add to 810g of water to make 10% solution. Then 810+x g is the amount of new solution. Thus,

810+x - 100%,

x - 10%.

Mathematically,

\dfrac{810+x}{x}=\dfrac{100}{10},\\ \\10(810+x)=100x,\\ \\8100+10x=100x,\\ \\100x-10x=8100,\\ \\90x=8100,\\ \\x=\dfrac{8100}{90}=90\ g.

So 90 g of water should be added and he will make 810+90=900 g of solution.

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\rule{130}1

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Let the two consecutive positive odd numbers be x and (x + 2)

\rule{130}1

☯ \underline{\boldsymbol{According\: to \:the\: Question\:now :}}

:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup

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\bullet\: \textsf {x = } \textbf {15}

\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17}

\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.

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