1. John’s age is three times that of his sister. When you add John’s age to his sister's age, you get 36. How old are John and h
is sister? (a) Write an equation that represents the situation. (1 point)
(b) Solve the equation from Part (a). Show your work. (3 points)
Answer:
Part A: Write an equation.
If the present age is y, then n times the present age = ny.
If the present age is x, then age n years later/hence = x + n.
If the present age is x, then age n years ago = x – n.
The ages in a ratio a: b will be ax and bx.
A(S) + 12 = 3 * A(S), subtracting A(S) from both sides one gets 12 = 2 * A(S). Now dividing both sides by 2 we get A(S) = 12/2 = 6 . Therefore, the age of the sister is 6 years when her brother John is three times as old, that is 18 years.
To get the height to the nick we use the trigonometry formula: tan θ=opposite/adjacent θ=73° opposite=h ft adjacent=38 ft plugging our values we get: tan 73=h/38 thus h=38 tan 73 h=124.29~124.3 ft
