Answer
$7$ One dollar bills,
$8$ Five dollar bills.
Work Step by Step
Let $n =$ number of one dollar bills, and $f=$ number of five dollar bills.
Knowing there are a total of 15 bills, then
$n + f = 15$ (Equation 1)
Knowing there is a total of 47 dollars, then the total value of the bills is:
$(1)n + 5f = 47
\\n +5f = 47$ (Equation 2)
Solving by elimination:
Subtract Equation 1 to Equation 2 to cancel out the $n$'s giving us:
$n + 5f - (n + f) = 47 -15
\\n+5f-n-f=32
\\4f=32$
Divide both sides of the equation by 4:
$\frac{4f}{4} = \frac{32}{4}
\\f=8$
Substitute $f = 8$ to $n + f = 15$ and solve:
$n+f=15
\\n + 8 = 15
\\n = 15-8
\\n=7$
Thus, there are $7$ one dollar bills and $8$ five dollar bills.
Alternatively, solving by substitution:
Make $f$ the subject by subtracting $n$ to both sides of the Equation 1, giving
$f = 15 - n $
Substitute $15 - n$ to $f$ in $n + 5f = 47$:
$n+5f=47
\\n + 5(15 - n) = 47$
Distribute 5:
$n + 75 - 5n = 47$
Collect like terms:
$-4n + 75 = 47$
Subtract $75$ to both sides:
$-4n = -28$
Divide both sides by $-4$:
$n = 7$
Substitute in $n = 7$ to $f = 15 - n$ giving
$f = 15 - 7 = 8$
Thus, $n = 7$, $f = 8$
