A newspaper carrier has $6.40 in change. He has two more quarters than dimes but four times as many nickels as quarters. How many of each type does he have?

Question

Linear equation Word problem help

Answer 1

First, notice that $6.40 = 640 cents. The corresponding linear equation and a solution is shown below in several steps:

Original equation for amount of Dimes (D):

10*D  + 25*(D+2) +5*4*(D+2) = 640

Simplified as following, resulting in the answer for D:
55*D=550
D=10
thus having the amount of Quarters:
Q=12
and correspondingly, amount of Nickels:
N= 48
The equation can be easily solved online using Linear Equation Solver (http://examn8.com)

Hope this will help. Best regards,

Answer 2

                    Quarters               dimes               Nickles

6.40 = 0.25*(dimes +2) + 0.10* dimes + 0.05 * 4*(dimes + 2)

 

6.40 - 2*0.25 - 0.05 * (4 * 2) = 0.25 dimes + 0.10 dimes + 0.05 * 4 * dimes

 

5.50 = dimes * ( 0.25 + 0.10 + 0.05 * 4 )

 

5.50 = dimes * 0.55

 

dimes = 5.50 / 0.55 = 10 dimes

 

Quarters = 10 + 2 = 12 Quarters

 

nickles = 4 x 12 = 48 Nickles