i have 32 coins in my pocket. all consisting of dimes and nickels. they add up to $2.45. how many dimes do i have ? and how many nickels do i have ?

Question

There much be two variables. one variable will be dimes value, and one variable with be the nickels value (lets statements). Also you must make two equations 

Answer 1

To make a system of equations to solve this problem, lets let d = # of dimes and n = # of nickels.  Since we know there are 32 coins in the pocket our first equation would be d + n = 32.  Now we need to set up a value equation.  Since dimes are $.10 we will write .10d and since nickels are $.05 we will write .05n.  Those two values need to add up to a total of $2.45 so the next equation will be .10d + .05n = 2.45.  To make our system of equations easier we can get rid of the decimals in the value equations by multiplying all terms by 100 to get 10d + 5n = 245.  Now our two equations are d + n = 32 and 10d + 5n = 245.  If we multiply all our terms in our first equation by -10 we will get -10d - 10n = -320 and if we add that vertically to the equation 10d + 5n = 245 our d terms cancel out leaving -5n = -75.  Divide both sides by - 5 you will get 15, so there are 15 nickels.  Go back to our first equation d + n = 32 and substitute 15 for n and now you have d + 15 = 32.  Subtract 15 from both sides you obtain d = 17, which means there are 17 dimes.  Now to check your work substitute both your new n and d into the value equation .10d + .05n = 2.45 to see if it works.  .10(17) = 1.70 and .05(15) = 0.75 and 1.70 + 0.75 is 2.45.  Our check works.