COIN WORD PROBLEM

Question

A newspaper carrier has 3.20 in change he has 4 more quarters than dimes but has 5 times as many nickels as quarters. How many coins of each does he have

Answer 1

Hi Renee;

Total...$3.20

x=quantity of dimes

quarters...(0.25)(x+4)

dimes...(0.10)(x)

nickles...(5)(0.05)(x+4)

3.20=[(0.25)(x+4)]+[(0.10)(x)]+[(5)(0.05)(x+4)]

3.20=0.25x+1.00+0.10x+0.25x+1.00

Combine like terms...

3.20=0.60x+2.00

Let's subtract 2.00 from both sides...

3.20-2.00=0.60x+2.00-2.00

1.20=0.60x

Let's divide both sides by 0.60...

1.20/0.60=(0.60x)/0.60

2=x

 

quantity of quarters...2+4=6

quantity of dimes...2

quantity of nickles...(5)(6)=30

 

Let's check our work...

3.20=[(6)(0.25)]+[0.10)(2)]+[(0.05)(30)]

3.20=1.50+0.20+1.50

3.20=3.20

Answer 2

Q = D + 4

 

N = 5 Q

 

0.25Q + 0.10D + 0.05N = 3.20

 

25Q + 10D + 5N = 320

 

25Q + 10(Q-4) + 5(5Q) = 320

 

25Q + 10Q - 40 + 25Q = 320

60Q = 360

 

Q = 6

 

D = Q - 4 = 2

 

N = 5 Q = 30

 

check:

 

0.25*6 + 0.10*2 + 0.05*30 =? 3.20

 

1.50 + 0.20 + 1.50 =? 3.20

 

3.20 = 3.20   √