Question

A cashier has a total of 133 bills, made up of fives and tens. The total value of the money is $705. How many ten-dollar bills does the cashier have?

Answer 1

There are 8 ten dollar bills

133-8=125
125x5=625
8x10=80
625+80=705

Answer 2

f = amount of five dollar bills

t = amount of ten dollar bills

so, he has a total of 133, thus whatever "f" and "t" are, we know that f + t = 133.

how much money is there in "f" amount of fives? well, 5*f, or 5f.
how much money is there in "t" amount of tens? well 10*t or 10t.

we know the total amount is 705, therefore 5f + 10t = 705.


`\bf \begin{cases} f+t=133\implies \boxed{f}=133-t\\ 5f+10t=705\\ -------------\\ 5\left( \boxed{133-t} \right)+10t=705 \end{cases} \\\\\\ 665-5t+10t=705\implies 5t=40\implies t=\cfrac{40}{5}\implies t=8`

how many fives are there? well, f = 133 - t.