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

Algebra ->  Percentage-and-ratio-word-problems -> 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       Log On


   

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(52754) About Me  (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?
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Let x be the amount she had at first.


Then at the end she had  x - %281%2F5%29x - %282%2F3%29x + 171 = x - %283%2F15%29x - %2810%2F15%29x + 171 = %282%2F15%29x + 171.


Your equation is 


    %28%28%282%2F15%29x%2B171%29%29%2Fx = 7%2F5.


Cross multiply, simplify and find x


    5%28%282%2F15%29x+%2B+171%29 = 7x

    %2810%2F15%29x+%2B+5%2A171 = 7x

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

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

    15*5*171 = 95x

    x = %2815%2A5%2A171%29%2F95 = 135.


ANSWER.  At first, Kathleen had 135 dollars.

Solved.