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Harlamova29_29 [7]

3 years ago

10

A chemist needs a 70% solution of tannic acid. How much distilled water must he add to 5 gallons of a 90% solution of acid to ob

tain the 70% solution?

1 answer:

kolezko [41]3 years ago

6 0

<span>4.5 + 0 = 3.5 + 0.7x
1 = 0.7x
x = 1/0.7
x = 1.43 gallons of distilled water
Hope this helps!!</span>

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What is the correct first step to solve this system of equations by elimination?

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$\bold{\huge{\pink{\underline{ Solution }}}}$

$\bold{\underline{ Given }}$

<u>We </u><u>have </u><u>given </u><u>two </u><u>linear </u><u>equations </u><u>that</u><u> </u><u>is </u><u>2x </u><u>-</u><u> </u><u>3y </u><u>=</u><u> </u><u>-</u><u>6</u><u> </u><u>and </u><u>x</u><u> </u><u>+</u><u> </u><u>3y </u><u>=</u><u> </u><u>1</u><u>2</u><u> </u><u>.</u>

$\bold{\underline{ To \: Find }}$

<u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>x </u><u>and </u><u>y </u><u>by </u><u>elimination </u><u>method</u><u>. </u>

$\bold{\underline{ Let's \: Begin }}$

$\sf{ 2x - 3y = -6 ...eq(1)}$

$\sf{ x + 3y = 12 ...eq(2)}$

<u>Multiply </u><u>eq(</u><u> </u><u>2</u><u> </u><u>)</u><u> </u><u>by </u><u>2</u><u> </u><u>:</u><u>-</u>

$\sf{ 2( x + 3y = 12 )}$

$\sf{ 2x + 6y = 24 }$

<u>Subtract </u><u>eq(</u><u>1</u><u>)</u><u> </u><u>from </u><u>eq(</u><u>2</u><u>)</u><u> </u><u>:</u><u>-</u>

$\sf{ 2x + 6y -( 2x - 3y) = 24 -(-6)}$

$\sf{ 2x + 6y - 2x + 3y = 24 + 6 }$

$\sf{ 9y = 30 }$

$\sf{ y = 30/9}$

$\sf{\red{ y = 10/3}}$

<u>Now</u><u>, </u><u> </u><u>Subsitute</u><u> </u><u>the </u><u>value </u><u>of </u><u>y </u><u>in </u><u>eq(</u><u> </u><u>1</u><u> </u><u>)</u><u>:</u><u>-</u>

$\sf{ 2x - 3(10/3) = -6 }$

$\sf{ 2x - 10 = -6 }$

$\sf{ 2x = -6 + 10}$

$\sf{ x = 4/2}$

$\sf{\red{ x = 2}}$

Hence, The value of x and y is 2 and 10/3

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