Question

Harvey has some 1 bills and some 5 in all he has 6 bills worth 22 let x be the number of 1 bills and let y be the number of 5 bills write a system of equations to represent the information and use substitution

Answer 1

We can write two equations to represent the information given. The first equation represents the total number of bills and the second equation represents the total amount of money:

x + y = 6 (the number of 1 bills plus the number of 5 bills is 6)

1x + 5y = 22 (the total amount of money is 22)

We can use substitution to solve for one of the variables in terms of the other and then substitute that expression back into one of the equations to find the other variable.

From the first equation, we can solve for y in terms of x:

y = 6 - x

Substituting this expression for y into the second equation, we have:

1x + 5(6 - x) = 22

Expanding the right side:

1x + 30 - 5x = 22

Combining like terms:

-4x + 30 = 22

Subtracting 30 from both sides:

-4x = -8

Dividing both sides by -4:

x = 2

So, there are 2 one dollar bills. To find the number of 5 dollar bills, we can substitute x = 2 back into the equation we derived for y:

y = 6 - x = 6 - 2 = 4

So, there are 4 five dollar bills.