Ayana has $2.35 in nickels and dimes. If she has 33 coins in all, find the number of nickels and dimes.

Question

 Make an equation and show the work

Answer 1

Hi Ayana,

A nickel is worth 5¢ and a dime worth 10¢, $2.35 is 235¢

If x is number of nickels and y the number of dimes

x + y   =33, x = 33 - y

5x +10y=235  substitute for x

5(33 -y) +10y =235

165 - 5y+ 10y =235

                  5y  = 70

y = 14 and x = 19

There are  14 dimes and 19 nickels

Answer 2

Let's star with what the question tells us...

- there is some unknown number of nickles... since nickles are worth 5 cents we can write the value of this part of the money as an X amount of 5 or 5x

- there is some unknown number of dimes...  dimes are worth 10 cents so lets label its unknown amount as Y and write this part of the money as 10y

- the total amount of money is $2.53 which we can also write as 253 cents

 

You now have 2 parts and a total to write an equation.

 

- you also know that the number nickles and the number of dimes total 33

 

Now you can make a second equation

 

Each of your equations have 2 unknowns x and y.  Solve one equation for x or y and then use substitution.

 

*Pay attention to words like 'total' to help you set up your equation*

Answer 3

suppose it has x nickels and then number of dimes will be 33-x

 

5x + (33-x)*10 = 235

 solve for x, x = 19, the 33-19=14.

 

so there will be 19 nickels and 14 dimes.