Maryam’s wallet contains a combination of $5 and $10 bills. what is the ratio of $5 bills to $10 bills? (1) the ratio of the number of bills to the total dollar value is 1/9. (2) the total dollar value of the bills is $360.

(1) The ratio of number of $5-bill to number of $10-bill is: 1/4;

(2) The ratio of number of the $5-bill to number of $10-bill is: x/ [(72-x)/2] in which x is the number of $5-bill and x must be either 0 or an even positive integral ( as their is insufficient information given, there can be many ratios that suit into the given information as long as the condition on x is met).

Step-by-step explanation:

(1) Denote x is the number of $5 bill and y is the number of $10 bill, in which x and y should be >= 0 and is an integral number.

We have (x+y) / (5x + 10y) = 1/9 <=> 9x + 9y = 5x + 10y <=> 4x = y <=> x/y =1/4 .

(2) Denote x is the number of $5 bill, y is the number of $10 bill.

We have: 5x + 10y = 360 <=> x = [ 360 - 10y ] /5 <=> x = 72 - 2y <=> y = (72 - x)/2 => x/y = x/[(72-x)/2] in which x must be must be either 0 or an even positive integral so that y can be identified in order to match with the given information .

answer: 177/8

step-by-step explanation:

(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