CH-10-001 · Combined proportion and percentage change
y is directly proportional to the square root of t. When t = 49, y = 21. Also, t is inversely proportional to the square of x. When x = 3, t = 49. Find a formula for y in terms of positive x. Then find the percentage decrease in y when x increases by 25%. Give the percentage to 2 decimal places.
Combined Direct & Inverse Proportion + Percentage Change
Booklet p. 23 & p. 52
Method
1) Write y = k₁√t and t = k₂/x² and find constants
2) Substitute t into y and simplify
3) Replace x with (1 + %/100)x to find percentage decrease
Worked Example (CH-10-001)
1)
y = 3√t.
2)
3)
Substitute and simplify using x > 0.
4)
5)
New y / old y = 1 ÷ 1.25.
6)
Decrease 20.00%.
Ans =
; decrease 20.00%.