Find an equation and solve

Question

Elizabeth has twice as many nickels as dimes, and four times as many pennies as nickels. If she has a total of $2.80, how many of each coin does she have?

Answer 1

Elizabeth has twice as many nickels as dimes:

n = 2d    {equation 1}

 

four times as many pennies as nickels:

p = 4n = 4(2d) = 8d    {equation 2}

 

she has a total of $2.80:

0.01p + 0.05n + 0.10d = 2.80    {equation 3}

 

Equation 3 will be easier to deal with if we multiply both sides through

by 100 to clear the decimals

 

p + 5n + 10d = 280

 

Replace n with 2d and replace p with 8d and solve for d.

 

8d + 5(2d) + 10d = 280

28d = 280

d = 10 dimes

n = 2d = 20 nickels

p = 8d = 80 pennies

 

Check:  0.01p + 0.05n + 0.1d = 2.8

           0.01(80) + 0.05(20) + 0.10(10) =

           0.80 + 1 + 1 = 2.80

           2.80 = 2.80