Question 1184141
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Kathleen had some money at first. She spent 1/5 of it on a watch and 2/3 of it on a handbag. 
After that, her grandparents gave her $171. The ratio of the total amount of money she had at the end 
to the amount of money she had at first was 7:5. How much money did Kathleen have at first?
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Let x be the amount she had at first.


Then at the end she had  x - {{{(1/5)x}}} - {{{(2/3)x}}} + 171 = x - {{{(3/15)x}}} - {{{(10/15)x}}} + 171 = {{{(2/15)x}}} + 171.


Your equation is 


    {{{(((2/15)x+171))/x}}} = {{{7/5}}}.


Cross multiply, simplify and find x


    {{{5((2/15)x + 171)}}} = 7x

    {{{(10/15)x + 5*171}}} = 7x

    10x + 15*5*171= 7*15*x

    15*5*171 = 7*15x - 10x

    15*5*171 = 95x

    x = {{{(15*5*171)/95}}} = 135.


<U>ANSWER</U>.  At first, Kathleen had 135 dollars.
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Solved.