Answers

1. Answer:  15 nickels and 20 dimes

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   Work Shown:

   n = number of nickels

   d = number of dimes

   d = 2n-10 since “number of dimes is 10 less than twice the number of nickels”

   0.05n = value of all the nickels in dollars

   0.10d = value of all the dimes in dollars

   0.05n+0.10d = total value in dollars

   0.05n+0.10d = 2.75

   Multiply all three terms by 100 to move the decimal point over two spots to the right. We get this new updated equation

   5n+10d = 275

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   Now plug in d = 2n-10 and solve for n

   5n+10d = 275

   5n+10(2n-10) = 275

   5n+20n-100 = 275

   25n-100 = 275

   25n = 275+100

   25n = 375

   n = 375/25

   n = 15

   There are 15 nickels.

   Use this to find the value of d.

   d = 2n-10

   d = 2*15-10

   d = 30-10

   d = 20

   There are 20 dimes.

   ———–

   Check:

   5n = 5*15 = 75 cents from just the nickels only

   10d = 10*20 = 200 cents from just the dimes only

   5n+10d = 75+200 = 275 cents total

   275 cents = 275/100 = $2.75

   This confirms the answers.

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