I am working on this problem and I just cannot get it. Jane has some nickels, di

Question

I am working on this problem and I just cannot get it. Jane has some nickels, dimes, and quarters which total $1.90.She has twice as many quarters as dimes. She has three times asmany quarters as nickels. How many quarters does she have? Thanks for helping! I am working on this problem and I just cannot get it. Jane has some nickels, dimes, and quarters which total $1.90.She has twice as many quarters as dimes. She has three times asmany quarters as nickels. How many quarters does she have? Jane has some nickels, dimes, and quarters which total $1.90.She has twice as many quarters as dimes. She has three times asmany quarters as nickels. How many quarters does she have? Thanks for helping!

Explanation / Answer

Jane has some nickels, dimes, and quarters which total$1.90.
.05N + .10D + .25Q = 1.90    multiply by 100across 1) 5N + 10D +25Q =190    simplify by dividingby 5 across 1) N + 2D + 5Q = 38 She has twice as many quarters as dimes. Q = 2D   rewrite 1) with Q = 2D 1b) N + 2D +5(2D) = 38 1b)  N +12D   = 38 She has three times as many quarters as nickels. Q= 3N      rewrite 1) with Q=3N 1c) N + 2D +5(3N ) = 38 1c) N + 2D +15N   = 38 1c) N + 2D +15N   = 38 1c) 16N +2D    =38     divide across by 2 1c) 8N +D    = 19 1c) 8N +D    = 19 How many quarters does she have? Put 1b) and 1c) together and solve for d 1b)  N +12D   = 38     multiply by-8 1c) 8N +D    = 19        1c)   8N   +  D    = 19 1b)  -8 N-96D   = -304   add 1b) and 1c)                -95D   =-285                divide by -95                      D =3          Put this into 1c) solve for N 1c) 8N+ 3    = 19    1c) 8N     = 16 N = 2 D =3   put into 1) solve forQ 1) N + 2D + 5Q =38          2   +2(3) + 5Q = 38
        2 + 6 + 5Q =38
               8 + 5Q =38              subtract 8 from both sides                      5Q = 30                          Q= 6 N = 2   D = 3 check: .05(2) + .10(3) + .25(6) = 1.90 .10    + .30    +1.50    = 1.90 check: .05(2) + .10(3) + .25(6) = 1.90 .10    + .30    +1.50    = 1.90            

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