Question 518958


40 coins =$4.05  Have 7 more nickles than dimes. how many quarters do yo have?


Let the amount of quarters be Q, and dimes D
Then the amount of nickels = D + 7


We can then say that: D + D + 7 + Q = 40 ----- 2D + Q = 33 -------- eq (i)


Also, .1D + .05(D + 7) + .25Q = 4.05 ----- .1D + .05D + .35 + .25Q = 4.05 ---- .15D + .25Q = 3.7 -------- eq (ii)


2D + Q = 33 -------- eq (i)
.15D + .25Q = 3.7 -------- eq (ii)
- 6D – 3Q = - 99 ------- Mutiplying eq (i) by – 3 -------- eq (iii)
6D + 10Q = 148 ------- Mutiplying eq (ii) by 40 --------- eq (iv)
7Q = 49 --------- Adding eqs (iii) & (iv)


Q, or amount of quarters = {{{49/7}}}, or {{{highlight_green(7)}}}


2D + 7 = 33 ------ Substituting 7 for Q in eq (i)
2D = 26


D, or amount of dimes = {{{26/2}}}, or {{{highlight_green(13)}}}


Therefore, amount of nickels = {{{highlight_green(20)}}} (13 + 7)


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Check
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13 dimes = $1.30
20 nickels = $1.00
7 quarters = $1.75 


$1.30 + 1.00 + 1.75 = $4.05


$4.05 = $4.05 (TRUE)


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