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777dan777 [17]
3 years ago
12

Sarah has a collection of nickels, dimes, and quarters worth $22.25. She has 10 more dimes than nickels and twice as many quarte

rs as dimes. How many coins of each kind does she have?
Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0

She has 35 dimes, 25 nickels and 70 quarters.

<u><em>Explanation</em></u>

Suppose, the number of dimes is x

As there is 10 more dimes than nickels, that means <u>number of nickels is 10 less than dimes</u>. So the number of nickels =x-10

Also, there is <u>twice as many quarters as dimes</u>. So, the number of quarter =2x

We know that, <u>value of each dime, nickel and quarter are  $0.10 , $0.05 and $0.25</u>

The total value of all coins is given as $22.25   So, the equation will be......

0.10x+0.05(x-10)+0.25(2x)=22.25\\ \\ 0.10x+0.05x-0.5+0.50x =22.25\\ \\ 0.65x=22.25+0.5\\ \\ 0.65x=22.75\\ \\ x=\frac{22.75}{0.65}=35

So, the number of dimes is 35 , the number of nickels is (35-10)= 25 and the number of quarters is (2×35)= 70

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