Question 364357: warren has 40 coins (all nickels, dimes, and quarters) worth 4.05. He has 7 more nicles than dimes. how many quarters does he have?
Answer by amoresroy(361)   (Show Source):
You can put this solution on YOUR website! warren has 40 coins (all nickels, dimes, and quarters) worth 4.05. He has 7 more nicles than dimes. how many quarters does he have?
Let Q = number of quarters
N = number of nickels
D = number of dimes
N = D + 7
Equation 1 is
Q + N + D = 40
Substite N = D + 7
Q + (D+7) + D = 40
Q + 2D = 40-7
Q + 2D = 33
2D = 33 - Q
D = 16.5 - .5Q
Equation 2 is
.25Q + .05N + .10D = 4.05
Substite N = D + 7
.25Q + .05(D+7) + .10D = 4.05
.25Q +.05D + .35 + .10D = 4.05
.25Q + .15D = 4.05 - .35
.25Q + .15D = 3.7
Since D = 16.5 - .5Q in equation 1
.25Q + .15D = 3.7 (in equation 2) becomes
.25Q + .15(16.5-.5Q) = 3.7
.25Q + 2.475 - .075Q = 3.7
.175Q = 3.7 - 2.475
Q = 1.225/.175
Q = 7
D = 16.5 - .5(7) = 13
N = D + 7 = 13 + 7 = 20
To check:
.25(7) + .05(20) + .10(13) = 4.05
Warren has 7 quarters
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