word problem,

Question

A bank teller has 112 $5 and $10 bills for a total of $720. How many of each kind does he have?

Answer 1

Number of $10 = x

 

number of $5=y

 

x+y=112          ________eq 1

 

10x+5y=720   ________eq 2

 

x+y=112

 

x=112-y

 

substitute value of x in eq 2

10(112-y)+5y=720

1120-10y+5y=720

1120-5y=720

 

5y=400

y=80

 

x=112-80=32

 

Number of $10 = x =32

number of $5=y=80

Answer 2

Let f = # five dollar bills

Let t = # ten dollar bills

 

We can make a system of 2 simultaneous equations:

 

1)  f + t = 112          There are 112 total bills

2)  5f + 10t = 720     Total money is $720

 

We can solve by substitution or elimination.

Let's use elimination.

 

multiply equation 1 through by -5 and add the equations

 

-5f - 5t = -560

 5f +10t = 720

-------------------

       5t = 160

        t = 32

 

Since f+t = 112 and t = 32

f = 112-t = 112-32 = 80

 

There are 80 of the $5 bills and 32 of the $10 bills

 

 

Answer 3

This type of question occurs with great frequency on this website, on a continuing basis.

 

As ALWAYS, you begin by letting assigning variables; in this case, let f = # five-dollar bills & t = # of ten-dollar bills.

 

Then you write two equations--one giving the total # of bills, the other giving the value of this wealth.

 

Two equations, two unknowns (system of linear equations).  Solve by any method that you have learned.

 

You can search this website for similar problems, as well as any good textbook.