John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, #d#, in his pocket.?

1 Answer
May 1, 2018

#n = 4 + d#
#n + 2d = 25#

#d = 7#

Explanation:

In this case, you would not write an equation, you would write two equations. This will give you a system with two equations and two unknowns. The equations will be linearly independent, meaning you'll be able to use them to solve for #d#.

First, we know that John has four more nickels than dimes. Let #n# be the number of nickels and #d# the number of dimes. Then #n = 4+d# represents the relative amounts of nickels and dimes.

Additionally, we know that our change totals #$1.25#. Since dimes are worth 10 cents and nickels worth 5, this can be modeled with the equation #0.05n + 0.1d = 1.25#. To eliminate the decimals, we can multiply this through by 20 to yield #n + 2d = 25#.

We then have the two equations:
#n = 4 + d#
#n + 2d = 25#

We will substitute the first into the second, giving
#n + 2d = 25 -> (4+d) + 2d = 25 -> 3d = 21 -> d = 7#.

This gives us our answer; we have #7# dimes. (Plugging this value of #d# into the first equation also reveals that we have #11# nickels.)