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:

Total number of bills of one, five and ten = 165

Total amount = $893

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

To find:

Number of bills of each type.

Solution:

Let number of bills of one, five and ten are x, y and z respective.

Total number of bills of is 165.

$x+y+z=165$         ...(i)

Total amount is $893.

$1x+5y+10z=893$         ...(ii)

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

$y=2(x+z)$     ...(iii)

From equation (iii), we get

$\dfrac{y}{2}=x+z$       ...(iv)

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

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

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

$3y=330$

$y=110$

Putting y=110 in (iv), we get

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

$x+z=55$

$x=55-z$       ...(v)

Putting y=110 and x=55-z in (ii), we get

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

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

$9z+605=893$

$9z=893-605$

$9z=288$

Divide both sides by 9.

$z=32$

Putting z=32 in (v), we get

$x=55-32$

$x=23$

Therefore, the number of one, five and ten bills are 23, 110 and 32 respectively.

Answer 2

There are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

According to the given situation

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

Let the number of $1 bills be "x"

Let the number of $5 bills be "y"

Let the number of $10 bills be "z"

Total number of bills = x + y + z  

Also it is given that there are twice as many five dollar bills as there are ones and tens combined

hence we can write the equations in the form of 3 variables

$\rm x + y + z = 165........(1) \\x +5y + 10z = 893.........(2) \\y = 2\times (x+z) ..........(3)$

These are three linear equations  with 3 variables that can be solved for x, y and z .

On solving equations (1) , (2),  and (3) we get

$x = 23 \\y = 110 \\z = 32$

So we can conclude that there are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

For more information please refer to the link given below

https://brainly.com/question/21835898