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# Math Word Problem

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Bag A has 10 white towels and 35 blue towels. Bag B has 28 white towels and 40 blue towels. How many white towels and blue towels must be moves from Bag B to Bag A so that 4/5 of the towels in Bag A are blue and 3/4 of the towels in Bag B are white?

Aug 5, 2021

#1
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white : x

blue : y

$${24 - x \over 28 - x + 40 - y}{}{} =$$$${3\over 4}$$               $${28 - x \over 68-x-y}$$$$= {3 \over 4}$$
{                                         {
{     $${35 + y \over 10 + x 35 + y} =$$   $${4 \over 5}$$         { $${35 + y\over 45 + x + y}$$$$= {4 \over 5}$$

{ 3 * 18 - 3x - 3y = 4 * 28 - 4x

{ 4 * 45 + 4x + 4y = 34 * 5 + 5y

{ x = 7

{ y = 33

So white : 7         blue :  33

Aug 5, 2021