SOLUTION: 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

Question 1184141: 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?
Hi, can help please. Thanks
Answer by ikleyn(52756) (Show Source): You can put this solution on YOUR website!
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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?
~~~~~~~~~~~~~~~~

Let x be the amount she had at first.


Then at the end she had  x -  -  + 171 = x -  -  + 171 =  + 171.


Your equation is 


     = .


Cross multiply, simplify and find x


     = 7x

     = 7x

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

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

    15*5*171 = 95x

    x =  = 135.


ANSWER.  At first, Kathleen had 135 dollars.

Solved.

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