document.write( "Question 1188617: Patrick bought a bag of sweets.
\n" ); document.write( "3/8 of the sweets were apple-flavoured and the rest were
\n" ); document.write( "strawberry-flavoured.
\n" ); document.write( "After giving away 8/9 of the apple-flavoured sweets and 42
\n" ); document.write( "strawberry-flavoured sweets to his friends, he had 1/12 of the sweets
\n" ); document.write( "left.
\n" ); document.write( "Patrick paid $0.20 for each sweet.
\n" ); document.write( "How much did Patrick pay for the bag of sweets at first? \n" ); document.write( "

Algebra.Com's Answer #819745 by Shin123(626) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's say there are 3x apple-flavored sweets and 5x strawberry-flavored sweets.
\n" ); document.write( "Once Patrick gives away 8/9 of the apple-flavored sweets, he has $\"3x%2A%281-8%2F9%29=3x%2A1%2F9=x%2F3\"$ apple-flavored sweets left.
\n" ); document.write( "Patrick also gives away 42 strawberry-flavored sweets, so he has $\"x%2F3\"$ apple-flavored sweets and $\"5x-42\"$ strawberry sweets left.
\n" ); document.write( "We are given that he has 1/12 of his sweets left after this and $\"%283x%2B5x%29%2F12=2x%2F3\"$ . So we have $\"x%2F3%2B5x-42=2x%2F3\"$ .
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: x=9.
Graphical form: Equation $\"x%2F3%2B5x-42=2x%2F3\"$ was fully solved.
Text form: x/3+5x-42=2x/3 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+x%2F3%2B5x-42=2x%2F3+%29\"$
For tutors: simplify_cartoon( x/3+5x-42=2x/3 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+x%2F3+%29%2Bhighlight_red%28+5%2Ax+%29-42=2x%2F3\"$ .
Eliminated similar terms $\"highlight_red%28+x%2F3+%29\"$ , $\"highlight_red%28+5%2Ax+%29\"$ replacing them with $\"highlight_green%28+%281%2F3%2B5%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%281%2F3%2B5%29%2Ax+%29-42=2x%2F3\"$ .
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Look at $\"%28highlight_red%28+1%2F3+%29%2Bhighlight_red%28+5+%29%29%2Ax-42=2x%2F3\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+16%2F3+%29%29%2Ax-42=2x%2F3\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+16%2F3+%29%29%2Ax+%29-42=2x%2F3\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+16+%29\"$ , $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"highlight_green%28+16+%29%2Fhighlight_green%28+3+%29%2Ax-42=2x%2F3\"$ .
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Look at $\"16%2F3%2Ax-42=highlight_red%28+2%2Ax%2F3+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2Ax%2F3+%29\"$
It becomes $\"16%2F3%2Ax-42-highlight_green%28+2%2Ax%2F3+%29=0\"$ .
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Look at $\"16%2F3%2Ax-highlight_red%28+42+%29-2%2Ax%2F3=0\"$ .
Moved $\"-42\"$ to the right of expression
It becomes $\"16%2F3%2Ax-2%2Ax%2F3-highlight_green%28+42+%29=0\"$ .
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Look at $\"highlight_red%28+16%2F3%2Ax+%29-highlight_red%28+2%2Ax%2F3+%29-42=0\"$ .
Eliminated similar terms $\"highlight_red%28+16%2F3%2Ax+%29\"$ , $\"highlight_red%28+-2%2Ax%2F3+%29\"$ replacing them with $\"highlight_green%28+%2816%2A1%2F3-2%2A1%2F3%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%2816%2A1%2F3-2%2A1%2F3%29%2Ax+%29-42=0\"$ .
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Look at $\"%28highlight_red%28+16+%29%2Ahighlight_red%28+1+%29%2F3-2%2A1%2F3%29%2Ax-42=0\"$ .
Multiplied numerator integers
It becomes $\"%28highlight_green%28+16+%29%2F3-2%2A1%2F3%29%2Ax-42=0\"$ .
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Look at $\"%2816%2F3-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Ax-42=0\"$ .
Multiplied numerator integers
It becomes $\"%2816%2F3-highlight_green%28+2+%29%2F3%29%2Ax-42=0\"$ .
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Look at $\"%28highlight_red%28+16%2F3+%29-highlight_red%28+2%2F3+%29%29%2Ax-42=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+14%2F3+%29%29%2Ax-42=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+14%2F3+%29%29%2Ax+%29-42=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+14+%29\"$ , $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"highlight_green%28+14+%29%2Fhighlight_green%28+3+%29%2Ax-42=0\"$ .
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Look at $\"highlight_red%28+14%2F3%2Ax-42+%29=0\"$ .
Solved linear equation $\"highlight_red%28+14%2F3%2Ax-42=0+%29\"$ equivalent to 4.66666666666667*x-42 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=9.

Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "Since x=9, there were $\"9%2A8=72\"$ sweets at the beginning, so it cost Patrick $0.20*72=$14.40. \n" ); document.write( "

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