Answer: 19 quarters; 7 nickels
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Work Shown:
q = number of quarters
n = number of nickels
q+n = 26 because we have 26 coins that are quarters or nickels. Solve for q to get q = 26-n (subtract n from both sides). This will be used in the second equation to replace every copy of 'q' with '26-n'
25*q is the total value of all the quarters, and this value is in cents. Similarly, 5n is the total value of all the nickels (value in cents). The total value of all the coins is 25q+5n which is equal to 510 (since 510 cents = $5.10)
25q+5n = 510
25(q)+5n = 510
25(26-n)+5n = 510 .... replace q with 26-n (see above)
25(26)-25(n)+5n = 510 ... distribute
650-25n+5n = 510
650-20n = 510
650-20n-650 = 510-650 ... subtract 650 from both sides
-20n = -140
-20n/(-20) = -140/(-20) ... divide both sides by -20
n = 7
There are 7 nickels
Use this to find q
q = 26-n
q = 26-7 .... replace n with 7
q = 19
and there are 19 quarters
= 0.75