Answer:
number of bills worth $5=3,number of bills worth $ 1=11
Step-by-step explanation:
Hello
we can define two equations to find the number of each type of bill
Step 1
Let
x=number of bills worth $5
y=number of bills worth $ 1
z=total numbers of bills
as described in the question
z=14
hence
x+y=14 ⇒ equation 1
Step 2
Total quantity of money she has in bills of worth $5=5x
Total quantity of money she has in bills of worth $1=1y
w=total she has in her wallet =5x+1y
as described in the question
w=$26
Hence
5x+1 y=26 ⇒ equation 1
Step 3
solve the system of equations
[tex](1) x+y=14 \\(2) 5x+1 y=26\\\\[/tex]
isolating x from each equation
from (1)
[tex]x+y=14\\(Eq\ 3)x=14-y[/tex]
Now, from (2)
[tex]5x+1 y=26\\5x=26-y\\[/tex]
(Eq 3)=(Eq 4), x=x
so
[tex]14-y=\frac{26-y}{5}[/tex]
solving for y
[tex]5(14-y)=26-y\\70-5y=26-y\\70-26=-y+5y\\44=4y\\y=\frac{44}{4}\\ y=11[/tex]
Now replace the value of y in (3) or (4)
[tex](Eq\ 4)x=\frac{26-y}{5}\\x=\frac{26-11}{5}\\x=\frac{15}{5} \\x=3[/tex]
Hence
x=number of bills worth $5=3
y=number of bills worth $ 1=11
Have a nice day
