Question 168878This question is from textbook Intermediate Algebra
: I need help please.
This question was answered but I was not given full details/explanation how this problem was solved. I still don't know what to do. I NEED A FULL EXPLANATION STEP BY STEP. SO I CAN DO THESE TYPE OF PROBLEMS ON MY OWN.
Please Help. Thank You.
Nana Nantambu found some coins while looking under her sofa pillows. There were equal numbers of nickels and quarters, and twice as many half dollars as quarters. If she found $2.60 in all, how many of each denomination of coin did she find?
SECOND QUESTION:
Please Help Me. I tried every solution possible.
Otis Taylor has a box of coins that he uses when playing poker with his friends. The box currently contains 44 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $4.37. How many of each denomination of coin does he have in the box?
This question is from textbook Intermediate Algebra
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Nana Nantambu found some coins while looking under her sofa pillows. There were equal numbers of nickels and quarters, and twice as many half dollars as quarters. If she found $2.60 in all, how many of each denomination of coin did she find?
.
Let x = number of nickels or number of quarters
from: "twice as many half dollars as quarters"
2x = number of half dollars
.
Because we know the total is $2.60:
2.60 = .05x + .25x + .50(2x)
2.60 = .05x + .25x + x
2.60 = 1.30x
2 = x (number of nickels:number of quarters)
.
Half dollars:
2x = 2(2) = 4
.
Solution:
2 nickels, 2 quarters, and 4 half dollars
.
SECOND QUESTION:
Otis Taylor has a box of coins that he uses when playing poker with his friends. The box currently contains 44 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $4.37. How many of each denomination of coin does he have in the box?
.
Similar problem...
Let x = number of pennies or number of dimes
then, because we know there is a total of 44 coins:
"total coins" - "number of pennies" - "number of dimes" = "number of quarters"
44 - x - x = number of quarters
44 - 2x = number of quarters
.
Because the total was $4.37:
4.37 = .01x + .10x + .25(44 - 2x)
4.37 = .11x + .25(44 - 2x)
4.37 = .11x + (11 - .5x)
4.37 = .11x + 11 - .5x
4.37 = 11 - .39x
-6.63 = -.39x
17 = x (number of pennies and dimes)
.
quarters:
44 - 2x = 44 - 2(17) = 44 - 34 = 10 (quarters)
.
Solution:
17 pennies, 17 dimes, and 10 quarters
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