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A girl has been getting her parents change every day for a year. She has dimes and quarters worth $37.40. If she has six times as many dimes, how many of each coin does she have?



Answer :

Let the girl has 'x' dimes and 'y' quarters.

Consider the following conversions,

[tex]\begin{gathered} 1\text{ dime=10 cents} \\ 1\text{ quarter=25 cents} \\ 1\text{ dollar=100 cents} \end{gathered}[/tex]

Given that the number of dimes is six times the number of quarters,

[tex]\begin{gathered} x=6\times y \\ x=6y \end{gathered}[/tex]

Also, it is given that the total worth is $37.40,

[tex]\begin{gathered} 10x+25y=37.40\times100 \\ 10(6y)+25y=3740 \\ 60y+25y=3740 \\ 85y=3740 \\ y=44 \end{gathered}[/tex]

Then the value of 'x' is obtained as,

[tex]\begin{gathered} x=6(44) \\ x=264 \end{gathered}[/tex]

Thus, the girl has 264 dimes and 44 quarters.

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