The combined age of three relatives is 120 years. james is three times the age of dan, and paul is two time the sum of the ages of james and dan. how old is each person

Step-by-step explanation:

Let x represent Dan's age

3x be James'age

Paul 2(3x+x)=6x+2x

Suming all ages

x+3x+6x+2x=120

Solving for x

12x=120

x=10 (Dan's age)

3×=30 (James'age)

6×+2×=80(Paul's age)

35-60 students are taking math.

(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