Solve for v 0.0348=(v/342)/(v/342+(100-v)/1000)

Math
0.0348=v342v342+100-v1000
Rewrite the equation as v342v342+100-v1000=0.0348.
v342v342+100-v1000=0.0348
Factor each term.
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To write v342 as a fraction with a common denominator, multiply by 500500.
v342v342⋅500500+100-v1000=0.0348
To write 100-v1000 as a fraction with a common denominator, multiply by 171171.
v342v342⋅500500+100-v1000⋅171171=0.0348
Write each expression with a common denominator of 171000, by multiplying each by an appropriate factor of 1.
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Multiply v342 and 500500.
v342v⋅500342⋅500+100-v1000⋅171171=0.0348
Multiply 342 by 500.
v342v⋅500171000+100-v1000⋅171171=0.0348
Multiply 100-v1000 and 171171.
v342v⋅500171000+(100-v)⋅1711000⋅171=0.0348
Multiply 1000 by 171.
v342v⋅500171000+(100-v)⋅171171000=0.0348
v342v⋅500171000+(100-v)⋅171171000=0.0348
Combine the numerators over the common denominator.
v342v⋅500+(100-v)⋅171171000=0.0348
Rewrite v⋅500+(100-v)⋅171171000 in a factored form.
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Move 500 to the left of v.
v342500v+(100-v)⋅171171000=0.0348
Apply the distributive property.
v342500v+100⋅171-v⋅171171000=0.0348
Multiply 100 by 171.
v342500v+17100-v⋅171171000=0.0348
Multiply 171 by -1.
v342500v+17100-171v171000=0.0348
Subtract 171v from 500v.
v342329v+17100171000=0.0348
v342329v+17100171000=0.0348
Multiply the numerator by the reciprocal of the denominator.
v342⋅171000329v+17100=0.0348
Cancel the common factor of 342.
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Factor 342 out of 171000.
v342⋅342(500)329v+17100=0.0348
Cancel the common factor.
v342⋅342⋅500329v+17100=0.0348
Rewrite the expression.
v500329v+17100=0.0348
v500329v+17100=0.0348
Combine v and 500329v+17100.
v⋅500329v+17100=0.0348
Move 500 to the left of v.
500⋅v329v+17100=0.0348
Multiply 500 by v.
500v329v+17100=0.0348
500v329v+17100=0.0348
Solve for v.
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Multiply each term by 329v+17100 and simplify.
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Multiply each term in 500v329v+17100=0.0348 by 329v+17100.
500v329v+17100⋅(329v+17100)=0.0348⋅(329v+17100)
Cancel the common factor of 329v+17100.
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Cancel the common factor.
500v329v+17100⋅(329v+17100)=0.0348⋅(329v+17100)
Rewrite the expression.
500v=0.0348⋅(329v+17100)
500v=0.0348⋅(329v+17100)
Simplify 0.0348⋅(329v+17100).
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Apply the distributive property.
500v=0.0348(329v)+0.0348⋅17100
Multiply.
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Multiply 329 by 0.0348.
500v=11.4492v+0.0348⋅17100
Multiply 0.0348 by 17100.
500v=11.4492v+595.08
500v=11.4492v+595.08
500v=11.4492v+595.08
500v=11.4492v+595.08
Move all terms containing v to the left side of the equation.
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Subtract 11.4492v from both sides of the equation.
500v-11.4492v=595.08
Subtract 11.4492v from 500v.
488.5508v=595.08
488.5508v=595.08
Divide each term by 488.5508 and simplify.
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Divide each term in 488.5508v=595.08 by 488.5508.
488.5508v488.5508=595.08488.5508
Cancel the common factor of 488.5508.
v=595.08488.5508
Divide 595.08 by 488.5508.
v=1.21805142
v=1.21805142
v=1.21805142
Solve for v 0.0348=(v/342)/(v/342+(100-v)/1000)

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