SOLUTION: Hi If Bob had twice as many nickels and half as many quarters, he would have 60c less. Suppose he now has 16 nickels and quarters. How many of each coin does he have. Thanks

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Question 1191337: Hi
If Bob had twice as many nickels and half as many quarters, he would have 60c less. Suppose he now has 16 nickels and quarters. How many of each coin does he have.
Thanks
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

let nickels be n and quarters q
if he now has 16 nickels and quarters, then we have
n%2Bq=16
n=16-q
since
1n=5c+
1q=25c
total amont of cents will be 5%2816-q%29%2B25q

If Bob had twice as many nickels and half as many quarters,
2%285n%29%2B%2825q%29%2F2 he would have 60c less

2%285%2816-q%29%29%2B%2825q%29%2F2=5%2816-q%29%2B25q-60
q+=+8
=>n=8
check: total amount of cents
5%2816-8%29%2B25%2A8=240c
If Bob had twice as many nickels and half as many quarters,
2%2A5%2816-8%29%2B%2825%2A8%29%2F2=180c
difference:240c-180c=60c

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.
If Bob had twice as many nickels and half as many quarters, he would have 60c less.
Suppose he now has 16 nickels and quarters. How many of each coin does he have.
~~~~~~~~~~~~~~~ 

N = # of nickels

Q = # of quarters


Equations from the condition

    N + Q = 16                           (1)

    5*(2N) + 25%2A%28Q%2F2%29 = 5N + 25Q - 60    (2)


Simplify (2) by multiplying both sides of the equation by 2

    20N + 25Q = 10N + 50Q - 120

    10N - 25Q = -120

     2N -  5Q =  -24                    (3)


Thus we have the system of two equations, (1) and (3)

     N +  Q =  16      (1')

    2N - 5Q = -24      (3')


Solve by substitution. For it, express  Q = 16-N from (1') and substitute it into (3').

    2N - 5*(16-N) = -24 

    2N - 80 + 5N  = -24

      4N + 5N     = -24 + 80

         7N       =  56

          N       = 56/7 = 8.


ANSWER.  8 nickels and 16-8 = 8 quarters.



Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
If Bob had twice as many nickels and half as many quarters, he would have 60c less. Suppose he now has 16 nickels and quarters. How many of each coin does he have.
Thanks 
Let number of nickels be N
Then number of quarters = 16 - N
Amount of money: .05N + .25(16 - N) = - .2N + 4
If there were twice as many nickels, then number of nickels would be 2N

It there were twice as many nickels, then value of the nickels would be .05(2N) = .1N
If there were half as many quarters, then number of quarters would be matrix%281%2C3%2C+%2816+-+N%29%2F2%2C+or%2C+8+-+N%2F2%29
If there were half as many quarters, then the value of the quarters would be matrix%281%2C3%2C+.25%288+-+N%2F2%29%2C+%22=%22%2C+2+-+.25N%2F2%29

Since hypothetical scenario yields .60 less, we then get: 
                                                               .6N - .25N = 2.8 ------ Multiplying by LCD, 2
                                                                     .35N = 2.8
                                            Number of nickels, or 

                                            Obviously, number of quarters: 16 - 8 = 8