tom has a collection of 25 coins, some are dimes and some are quarters. If the total value of all the coins are $5.05, how many of each coin does tom have?

Question

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Answer 1

let q is the number of quartters and let d is the number of dimes

so it will be:  q + d  = 25  we know that a quarter represents the value of  0.25 $

and that the  a dime represents the value of 0.10 $

then it will be:  0.25q + 0.10d = 5.05  from the first equation we get q = 25 - d puttimg this to second equation

we get: 0.25(25-d) + 0.10d = 5.05  ->>>  6.25 - 0.25d + 0.10d = 5.05  ---->>>  -0.15d = -6.25 + 5.05  -->>>

-0.15d = -1.2  -->>>  -1.2/-0.15 = d  = 8  tom has 8 dimes. so 25-8 = 17 quarters

answer:  Tom has. 8 dimes  and  17 quarters