SOLUTION: Angel has $1.80 in nickels, dimes, and quarters in his pocket. He has twice as many quarters as nickels. The number of dimes in his pocket is one more than the number of nickels an

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Question 370108: Angel has $1.80 in nickels, dimes, and quarters in his pocket. He has twice as many quarters as nickels. The number of dimes in his pocket is one more than the number of nickels and quarters put together. Which set of three equations could be used to determine how many nickels, dimes, and quarters Angel has?
A) 5N + 10D + 25Q = 180
Q = 2N
D = N + Q + 1
B) 5N + 10D + 25Q = 180
N = 2Q
D = N + Q + 1
# 5N + 10D + 25Q = 1.80
Q = 2N
D + 1 = N + Q
# 0.05N + 0.10D + 0.75Q = 180
Q = 2N
D + 1 = N + Q
why is the answer A and not B?


Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"Angel has $1.80 in nickels, dimes, and quarters in his pocket. He has twice as many quarters as nickels. The number of dimes in his pocket is one more than the number of nickels and quarters put together. Which set of three equations could be used to determine how many nickels, dimes, and quarters Angel has?
A) 5N + 10D + 25Q = 180
Q = 2N
D = N + Q + 1
B) 5N + 10D + 25Q = 180
N = 2Q
D = N + Q + 1
# 5N + 10D + 25Q = 1.80
Q = 2N
D + 1 = N + Q
# 0.05N + 0.10D + 0.75Q = 180
Q = 2N
D + 1 = N + Q
why is the answer A and not B?"

$1.80 total in coins of nickels (N), dimes (D), and quarters (Q)
twice as many quarters as nickels --> Q = 2N
The number of dimes in his pocket is one more than the number of nickels and quarters put together. --> D = N + Q + 1
0.05N + 0.10D + 0.25Q = 1.80
5N + 10D + 25Q = 180
D = N + Q + 1 = N + 2N + 1 = 3N + 1
5N + 10(3N + 1) + 25(2N) = 180
5N + 30N + 10 + 50N = 180
85N + 10 = 180
85N = 170
N = 2, so 2 nickels
then Q = 4, so 4 quarters
then D = 7, so 7 dimes
check: 5(2) + 10(7) + 25(4) = 10 + 70 + 100 = 80 + 100 = 180, yes

answer A) 5N + 10D + 25Q = 180
Q = 2N
D = N + Q + 1
this matches with what we worked out above so it is the right answer

answer B) 5N + 10D + 25Q = 180 --> this line is right
N = 2Q --> this line is wrong, Q = 2N so N = Q/2
D = N + Q + 1 --> this line is right
# 5N + 10D + 25Q = 1.80 --> this line is wrong, the 1.80 should be 180
Q = 2N --> this line is right
D + 1 = N + Q --> this line is wrong, should be D - 1 = N + Q
# 0.05N + 0.10D + 0.75Q = 180 --> this line is wrong, should be 0.05N + 0.10D + 0.25Q = 1.80
Q = 2N --> this line is right
D + 1 = N + Q --> this line is wrong, should be D - 1 = N + Q