Question

You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?

Answer 1

Given:

You are given $893 in one, five, and ten dollar bills.

There are 165 bills.

There are twice as many five dollar bills as there are ones and tens combined.

To find:

How many bills of each type are there?

Solution:

Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.

According to the question,

Number of bills : $x+y+z=165$         ...(1)

Total amount : $1x+5y+10z=893$         ...(2)

Condition : $y=2(x+z)$     ...(3)

Equation (3) can be written as

$\dfrac{y}{2}=x+z$       ...(4)

Substituting $x+z=\dfrac{y}{2}$ in (1), we get

$\dfrac{y}{2}+y=165$

$\dfrac{3y}{2}=165$

$3y=330$

$y=110$

Substituting y=110 in (4), we get

$x+z=\dfrac{165}{2}$

$x+z=55$

$x=55-z$       ...(5)

Substituting y=110 and x=55-z in (2), we get

$(55-z)+5(110)+10z=893$

$55-z+550+10z=893$

$9z+605=893$

$9z=893-605$

$9z=288$

Dividing both sides by 9, we get

$z=32$

Substituting z=32 in (5), we get

$x=55-32$

$x=23$

Therefore,

One dollar bills = 23

Five dollars bills= 110

Ten dollars bills = 32