SOLUTION: Hi can you help me solve this problem please? "Coco has a jar containing pennies and nickels that add up to a total of $9.20. If she could switch the number of pennies with the n

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Question 1118952: Hi can you help me solve this problem please?
"Coco has a jar containing pennies and nickels that add up to a total of $9.20. If she could switch the number of pennies with the number of nickels, there would be $26.80 worth of coins in the jar. How many pennies and nickels are in the jar?"
Can you show the step by step solving progress for their problem? Thanks.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52807)   (Show Source): You can put this solution on YOUR website!
.
Let P the number of pennies and N be the number of nickels in the jar.


Then the coins worth is  P + 5N  cents  and the equation is


P + 5N =  920     (1)     (cents)


Now, under the "if" scenario, it would be P nickels and N pennies, that would worth 5P + N  cents.  So, the second equation is


5P + N = 2680     (2)    (cents)


Thus you have this system of two equation in 2 unknowns


P + 5N =  920     (1) 
5P + N = 2680     (2)


To solve it, from eq(1) express  P = 920-5N, and then substitute it into eq(2), replacing P. You will get a single equation for only one unknown N:


5*(920-5N) + N = 2680.


Simplify and solve for N:


4600 - 25N + N = 2680.


-24N = 2680 - 4600


-24N = -1920  ====>  N =  = 80.


Thus there are 80 nickels in the original collection.


Then the number of pennies is  P = 920 - 5N = 920 - 5*80 = 920 - 400 = 520.

Solved.


Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let n = number of nickels.
let p = number of pennies.

the number of cents in a nickel is 5.
the number of cents in a penny is 1.
the number of cents in a dollar is 100.

your first equation is 5n + p = 920.

if you switch the number of nickels with the number of pennies, then your second equation is 5p + n = 26.80.

re-arrange the variables so that your second equation reads n + 5p = 2680.

you have 2 equations that need to be solved simultaneously.

they are:

5n + p = 920
n + 5p = 2680

multiply the second equation by -5 to get:

5n + p = 920
-5n - 25p = -13400

add the 2 equations together to get:

-24p = -12480

solve for p to get:

p = 520.

in the first original equation of 5n + p = 920, replace p with 520 to get:

5n + 520 = 920

solve for n to get:

n = (920 - 520) / 5 = 80

replace n with 80 and replace p with 520 in both original equations to get:

5n + p = 920
n + 5p = 2680

become:

5*80 + 520 = 920
80 + 5*520 = 2680.

your solution is confirmed to be good.

it is:

number of nickels is 80 and number of pennies is 520 to get a total of 920 cents which is equal to $9.20.

number of nickels is 520 and number of pennies is 80 to get a total of 2680 cents which is equal to 26.80.

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