SOLUTION: I am a parent I want to help my child but i don't know how to do this. I'm not asking for the answer,(but i'm not turning it down either:>), but the necessary steps to take to solv

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Question 214173: I am a parent I want to help my child but i don't know how to do this. I'm not asking for the answer,(but i'm not turning it down either:>), but the necessary steps to take to solve this problem, so I may be able to help her. The question is Joshua had 142 coins, all nickels and quarters. The total amount was $15.30. HOw many coins of each type did he have? Solve this problem with Algebra using variables to stand for the number of nickels and the number of quarters. Thank you so much for whatever help you can provide me with. This question was not in a textebook.
Found 3 solutions by Alan3354, josmiceli, ankor@dixie-net.com:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Joshua had 142 coins, all nickels and quarters. The total amount was $15.30. HOw many coins of each type did he have?
-----------------
n + q = 142 (# of coins)
5n + 25q = 1530 (value of coins)
q = 142-n (from eqn 1)
Sub for q into eqn 2
5n + 25q = 1530
5n + 25(142-n) = 1530
5n + 3550 - 25n = 1530
-20n = -2020
n = 101 nickels
q = 41 quarters
--------------
101*5 + 41*25 = 505 + 1025
= 1530

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of quarters
Let = number of quarters
given:
(1)
(2) (in cents)
Multiply both sides of (1) by , and
subtract (1) from (2)
(2)
(1)


and, since



Hae has 41 quarters and 101 nickels
check answer:
(2)



OK
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Joshua had 142 coins, all nickels and quarters.
The total amount was $15.30.
HOw many coins of each type did he have?
:
Let n = no. of nickels; let q = no. of quarters
:
write an equation for each statement:
:
"Joshua had 142 coins,"
n + q = 142
:
"The total amount was $15.30."
.05n + .25q = 15.30
:
HOw many coins of each type did he have?
:
Go back to the 1st equation, and arrange it for substitution in the 2nd equation
n + q = 142
q = (142-n)
:
Replace q with (42-n) in the 2nd equation, find n
.05n + .25(142-n) = 15.30
:
Multiply what's inside the brackets
.05n + 35.5 - .25n = 15.30
;
.05n - .25n = 15.30 - 35.50
:
-.20n = -20.20
n = ; minus into a minus is plus
n = +101 nickels
:
Find q:
q = 142 - 101
q = 41 quarters
:
:
See if this is right, substitute for n and q
.05(101) + .25(41) = 15.30
5.05 + 10.25 = 15.30; confirms our solution
:
Make sense to you?
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