SOLUTION: Okay I am so lost on this question, so any help will be greatly appreciated. Philip has 10 coins in his pocket. Philip has the same number of pennies as quarters and the same

Question 184065: Okay I am so lost on this question, so any help will be greatly appreciated.
Philip has 10 coins in his pocket. Philip has the same number of pennies as quarters and the same number of dimes as nickels. He also has one more nickel than he does pennies. If he has 97 cents, how many coins of each type does he have?
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Philip has 10 coins in his pocket. Philip has the same number of pennies as quarters and the same number of dimes as nickels. He also has one more nickel than he does pennies. If he has 97 cents, how many coins of each type does he have?
---------------------------------------
Value Equation: p + 25q + 10d + 5n = 97
Quantity Eqations:
p = q
d = n
n = p + 1
--------------
Substitute to get an equation in "p":
p + 25p + 10(p+1) + 5(p+1) = 97
p + 40p + 15 = 97
41p = 82
p = 2 (# of pennies)
q = 2 (# of quarters)
n = 2+1 = 3 (# of nickels)
d = 3 (# of dimes)
-------------------------
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Philip has 10 coins in his pocket. Philip has the same number of pennies as
quarters and the same number of dimes as nickels. He also has one more nickel
than he does pennies. If he has 97 cents, how many coins of each type does he have?
:
let p, n, d, q = no. of pennies, nickels, dimes and quarter respectively
:
Write an equation for each statement:
:
"Philip has 10 coins in his pocket."
p + n + d + q = 10
:
" Philip has the same number of pennies as quarters"
p = q
:
" and the same number of dimes as nickels."
d = n
:
"He also has one more nickel than he does pennies."
n = (p + 1)
:
" If he has 97 cents,"
1p + 5n + 10d + 25q = 97
:
how many coins of each type does he have?
:
Using the given equations, replace p with q, and d with n in the 1st equation
q + n + n + q = 10
2n + 2q = 10
simplify, divide by 2
n + q = 5
n = (5-q) good for substitution
:
Do the same in the total value equation
1q + 5n + 10n + 25q = 97
15n + 26q = 97
:
Substitute (5-q) for n
15(5-q) + 26q = 97
75 - 15q + 26q = 97
11q = 97 - 75
11q = 22
q =
q = 2 quarters
:
we know p = q, therefore
p = 2 pennies
:
we also know n = p + 1, therefore
n = 3 nickels
:
we know d = n, therefore
d = 3 dimes
:
Check solution, in total coin equation
2 + 3 + 3 + 2 = 10
:
You can check solution in total value equation
1q + 5n + 10n + 25q =
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