Sally found a wallet while walking down the street the other day and it contained 11 bills in total. The wallet had only $5 bills, $10 bills and $20 bills in it. The total value of all the bills was 115, and the total of the $5 and $10 bills was $75. Define the variables using xyz.

x=3

y=6

z=2

Z is the number of $20 bill , y is the number of $ 10 bill and x is the number of $ 5bill

Step-by-step explanation:

Let the number of $5 bills be x,  number of$10 bills bey  and number of $20 bills be z in it.

Then

5x+ 10y+ 20z= 115A

5x+10y= 75B

Putting the values from A into B

75+ 20z= 115

20 z= 115-75

20z =40

z= 40/20 = 2

There were 2 bills of $ 20.

Now we are left with 9 bills which are of $5 and $10

so

x+y=9

or x= 9-yC

Putting C in B

5(9-y) + 10y = 75

45-5y+10y= 75

45+5y= 75

5y= 75-45

5y= 30

y= 6

So the number of $10 bills are 6.

And the number of $5 bills are 3

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

the answer is 40.

proof: