Question 625312

There are 27 nickels, dimes, and quarters in the drawer with a value of $3. How many coins of each type are there if there are three times as many nickels as there are dimes?


Let amount of nickels, dimes, and quarters be N, D, and Q, respectively


Then: N + D + Q = 27


Also, N = 3D, since there are 3 times as many nickels as dimes


Substituting 3D for N, we now have: 3D + D + Q = 27, or 4D + Q = 27 ----- eq (i)


Also, .05(3D) + .1(D) + .25(Q) = 3 ---- .15D + .1D + .25Q = 3 ---- .25D + .25Q = 3 ---- eq (ii)


4D + Q = 27 ----- eq (i)
- 4D - 4Q = - 48 ---- Multiplying eq (ii) by - 16 ----- eq (iii)
- 3Q = - 21 ------ Adding eqs (iii) & (i)


Q, or amount of quarters = {{{(- 21)/- 3}}}, or {{{highlight_green(7)}}}


4D + 7 = 27 ------ Substituting 7 for Q in eq (i)


4D = 20


D, or amount of dimes = {{{20/4}}}, or {{{highlight_green(5)}}}


Since there are 5 dimes, then there are 3 * 5, or {{{highlight_green(15)}}} nickels


Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com