coins for ryan

Question

Ryan has some nickels and dimes. Altogether, he has 34 coins that total $2.60. Write and solve a system of equations to determine how many of each coin he has.

Answer 1

Let N be the number of nickels he has and D be the number of dimes that he has.

So the first equation is N + D = 34, as is given in the problem he has 34 coins altogether.

 

Monetarily, the value of the nickel and dime in pennies, as you know, is 5 and 10, respectively.

So as given in the problem, he has $2.60, which is 260 pennies.

 

The second equation is then 5N + 10D = 260.

 

Solving the first equation for N results in N= 34 - D.

Substituting this expression for N into the second equation produces:

        5(34-D) + 10D = 260

         170 - 5D + 10D = 260   <-- distributive property

                 170 + 5D = 260    <-- combining like terms

                       5D = 90          <-- subtracts 170 from both sides

                       D = 18           <-- divides both sides by 5

 

 So he has 18 dimes, which means he has N = 34 - D = 34 - 18 = 16 nickels

 

 Note that 18 dimes is $1.80 while 16 nickels is $0.80 or 80 cents.

 This total is in fact $2.60

 

 Never forget to check the results you get like this. At the very least you know

 that the answer is correct. In later algebra problems, geometry, algebra 2, the checking

 of your solution to these types of equations will be MANDATORY, not optional.

 So my friendly advice as a teacher is to get into the habit of doing it now.