Applying a system of three

Question

A change purse contains $5.75 in nickels, dimes, and quarters. There are a total of 48 coins in the purse, and the number of nickels is 5 more than the number of quarters. How many of each type of coin are in the purse?

Answer 1

48 = n+d+q

5n+10d+25q = 575

10n+10d+10q = 480 subtract to eliminate d

-5n + 15q = 95 substitute 5+q = n

-5(5+q) + 15q = 95

-25 -5q +15q = 95

10q = 120

q = 12 quarters

n=17 nickels

d = 48-17-12 = 19 dimes

Answer 2

48 = n+d+q

5n+10d+25q = 575

10n+10d+10q = 480 subtract to eliminate d

-5n + 15q = 95 substitute 5+q = n

-5(5+q) + 15q = 95

-25 -5q +15q = 95

10q = 120

q = 12 quarters

n=17 nickels

d = 48-17-12 = 19 dimes

5(17)+10(19)+25(12) = 85+190+300 = 575

Answer 3

48 = n+d+q

5n+10d+25q = 575

10n+10d+10q = 480 subtract to eliminate d

-5n + 15q = 95 substitute 5+q = n

-5(5+q) + 15q = 95

-25 -5q +15q = 95

10q = 120

q = 12 quarters

n=17 nickels

d = 48-17-12 = 19 dimes