Question

A wallet has $420 in $5, $ 10 and $ 20 bills. the number of $5 bills exceeds twice the number of $10 bills by 4. the number of $20 bills is six fewer than the number of $ 10 many $ bills are there ?

Answer 1

There are 10 $10 bills in the wallet.

Step-by-step explanation:

Let's assume the number of $5 bills as x, the number of $10 bills as y, and the number of $20 bills as z.

From the given information, we can form two equations:

The number of $5 bills exceeds twice the number of $10 bills by 4:

x = 2y + 4.

The number of $20 bills is six fewer than the number of $10 bills:

z = y - 6.

We also know that the total amount in the wallet is $420.

We can express this as another equation:

Total amount = (value of $5 bills * number of $5 bills) + (value of $10 bills * number of $10 bills) + (value of $20 bills * number of $20 bills).

Plugging in the values, we get:

420 = (5 * x) + (10 * y) + (20 * z).

Now, we can substitute the values of x and z from equations 1 and 2 into equation 3:

420 = (5 * (2y + 4)) + (10 * y) + (20 * (y - 6)).

Simplifying this equation will give us the value of y, which is the number of $10 bills.

After solving the equation, we find that the number of $10 bills is 10.

Therefore,

Ten $10 bills in the wallet.

Answer 2

To find the number of $10 bills in the wallet, we set up a system of equations based on the information given and solved for the variable representing the number of $10 bills, which resulted in 13 $10 bills.

Step-by-step explanation:

The student's question involves solving a system of equations to find out how many $10 bills there are in a wallet containing $420 with $5, $10, and $20 bills, given certain conditions about the quantity of each bill type. Let's define our variables: Let x be the number of $10 bills, y be the number of $5 bills, and z be the number of $20 bills.

The conditions given are:

The number of $5 bills is four more than twice the number of $10 bills, so

y = 2x + 4.

The number of $20 bills is six fewer than the number of $10 bills, so

z = x - 6.

The total amount of money is $420, which leads to the equation

5y + 10x + 20z = 420.

Now, to find the number of $10 bills:

Substitute the expressions for y and z into the third equation:

5(2x + 4) + 10x + 20(x - 6) = 420.

Simplify the equation:

10x + 20 + 10x + 20x - 120 = 420.

Combine like terms:

40x - 100 = 420.

Add 100 to both sides:

40x = 520.

Divide by 40:

x = 13.

Therefore, there are 13 $10 bills in the wallet.