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

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!

let nickels be and quarters
if he now has nickels and quarters, then we have


since


total amont of cents will be

If Bob had twice as many nickels and half as many quarters,
he would have less



=>
check: total amount of cents

If Bob had twice as many nickels and half as many quarters,

difference:

Answer by ikleyn(53763)   (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) +  = 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)   (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 
If there were half as many quarters, then the value of the quarters would be 

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
RELATED QUESTIONS

harry has $2.25 in nickles, dimes, and quarters. If he had twice as many nickels, half as (answered by TimothyLamb,jsmallt9)
Craig has a total of $2.75 in nickels and quarters. He has twice as many quarters as... (answered by Alan3354,josmiceli)
Jeff has $1.30 in change. He has twice as many nickels as dimes. He has half as many... (answered by stanbon)
1. Joan has $3.50 in nickels, dimes and quarters. SHe has the same number of nickels as... (answered by solver91311)
Samuel has some quarters and some nickels. If he has nine more than twice as many nickels (answered by richwmiller)
Ryan has three times as many quarters as nickels. If Ryan had thirty-one more nickels and (answered by mananth)
1. Lisa has $1.75. She has twice as many nickels than dimes. How many of each. 2. Bob... (answered by solver91311,JBarnum)
Todd has some nickels, dimes, and quarters, which total $2.45. He has twice as many... (answered by Fombitz)
Caleb has $3.75 in dimes and nickels. If he has half as many nickels as he does dimes,... (answered by Alan3354)