Chapter 0.2, Problem 19E

To determine

To find: the number of bill deposited

Answer to Problem 19E

Thus, 3 bills of #5, l bill of $10 and 8 bills of $20 were deposited.

Explanation of Solution

Given:

A deposited 12 bills.

Calculation:

Register in form of table has some incomplete information which is to be completed. Table showing deposit is represented below.

Type of bill	No. deposited
$1	0
$5	X
$10	y
$20	z
Total	$175, 12 bills

Assume missing numbers to be x, y, z.

Now, formulating equations from conditions given,

  $x+y+z=12\mathrm{......}\left(1\right)$ {As there are 12 bills}

  $5x+10y+20z=175\mathrm{......}\left(2\right)$ {As total sum is $175}

As there are 3 unknowns and only 2 equations, thus, there can be many solutions. Only constraint is that they should be whole numbers.

Now, evaluating x and y in terms of z

Using, $\left(2\right)-5\times \left(1\right)$ ,

  $5y=\left\{60-5z\right\}-\left\{175-20z\right\}$

Or, $5y=15z-115$

Or, $y=3z-23$

Substituting this y in (1) to get x,

  $x=12-z-\left\{3z-23\right\}$

Or, $x=35-4z$

Since, x, y, z are whole numbers, trying various values of z by hit and trial, we get

z = 8

And, y = 1

And, x = 3

Thus, 3 bills of $5, l bill of $10 and 8 bills of $20 were deposited.

Conclusion:

Thus, 3 bills of $5, l bill of $10 and 8 bills of $20 were deposited.