Sherry's paycheck was $1300.00. When she cashed her check at the bank, the teller gave her a total of 25 bills, both hundreds and twenties. How many twenties did the teller give Sherry?

Question

2762 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-01T20:42:58

The teller would give Sherry 15 twenties and 10 hundreds.

We can solve this by setting up a system of equations. One for the number of bill and one for the value of the money.

The first equation is Hundreds + Twenties = 25 bills

$h + t = 25$ $h+t=25$

Since hundreds are worth $100 and twenties are worth $20 we can find the value by a second equation.

$100 h + 20 t = 1300$ $100h + 20t = 1300$

Now rearrange the first equation to isolate one of the variables.
$h = 25 - t$ $h=25-t$

Plug this equation in for $h$ $h$ in the second equation.

$100 (25 - t) + 20 t = 1300$ $100(25-t) + 20t = 1300$

Now use the distributive property to eliminate the parenthesis.
$2500 - 100 t + 20 t = 1300$ $2500-100t + 20t = 1300$

Now combine like terms.
$2500 - 80 t = 1300$ $2500 - 80t = 1300$

Use the additive inverse to isolate the variable term.
$cancel2500 - 80t cancel(-2500) = 1300 - 2500$

$-80t = -1200$

Use the multiplicative inverse to solve for $t$

$(cancel(-80)t)/cancel(-80) = -1200/-80$

$t = 15$ the number of twenties

$h=25-15$

$h = 10$ the number of hundrerds