HELP ME OUT PLEASE SOLVE IT

Question

HELP ME OUT PLEASE SOLVE IT..............
Jeannie has some $10 bills and some $20 bills.if she has 273 bills worth a total of $4370,how many of the bills are $10 bills and how many are $20 bills.?

 

 

Answer 1

X will represent the number of $10 bills.  Y will represent the number of $20 bills.

 

Step 1:  Set up a system of equations.  What do we know from the information given?  Well we know that Jeannie has $4370 total made up of a certain amount of $10 bills (X) and a certain amount of $20 bills (Y).  This is represented as: 10X + 20Y = 4370.  We also know that Jeannie has a total of 273 actual bills.  Some of them are $10 bills and some are $20 bills.  This is represented as: X + Y = 273.

 

Step 2: Solve for one of the variables first.  To do this, you will need to plug one of the equations into the other equation.  Let's solve for X first.  The equation X + Y = 273 can be simplified to Y = 273 - X.  Now, this can be plugged into the very first equation:

 

10X + 20(273 - X) = 4370

10X + 5460 - 20X = 4370

-10X + 5460 = 4370

-10X = -1090

     X = 109 ; So there are 109 $10 bills.

 

Now we can plug the solution for X into any of the equations to find Y.  Let's plug it into the most simple equation:       X + Y = 273.

                                          109 + Y = 273

                                           Y = 164 ; so there are 164 $20 bills.

 

To check your solution for accuracy, plug your results for both X and Y into the other equation:

                                        10X + 20Y = 4370

                                        10(109) + 20(164) = 4370

                                        1090 + 3280 = 4370

                                        4370 = 4370.  This is true, thus your X and Y results are correct.

 

 

Answer 2

Let x = number of 10 dollar bills and y = the number of 20 dollar bills. 

 

We have 2 equations. X+y=273 for the number of bills and 

10x+20y = 4370 for the value of the bills. Solving them simultaneously we substitute for x =273-y in the 2nd equation. 

 

10(273-y)+20y=4370

simplifying 

2730-10y+20y=4370

combing like terms on each side

 

10y=4370-2730

or y=164. 

Plugging 164 into the 1st equation 

 

gives x= 273-164=109. 

Can double check answer by plugging numbers back into 2nd equation and verify

 

10(109)+20(164)=4370 so it checks!