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Honors Algebra 2
Direct Variation
Variation Notes
Inverse Variation
Joint Variation
Name ____________________
Combined Variation
You will know if it is a variation problem because it will use one of the words, direct, inverse, joint or combined in the
problem.
Steps for solving:
Examples:
1) If y varies directly as x and y = 18 when x = 15, find y when
x = 20.
2) If a varies inversely as b and b = 4 when a = 16, find b when
a = 3.
3) If z varies directly as y and inversely as x, and z = 4 when y =
3 and x = 6, find x when z = 16 and y = 2.
4) If a varies jointly with b and c and inversely with d, find a
when b = 6, c = 7, and d = -4, if a = 3, b = 3, c = -2, and
d = -4.
5) Suppose a varies directly with b and inversely with the
square of c. If a = 12, b = 36, and c = 0.6, find a when
b = 97 and c = 0.2.
6) The length of rectangles of fixed area varies inversely as the
width. Suppose the length of a rectangle is 22 mm when the
width is 12 mm. Find the width when the length is 33 mm.
7) The area of a rectangle varies jointly as its length and width.
If the area of a rectangle is 72 cm2 when the length is 12 cm
and width is 6 cm, find the length when the area is 62.5 cm2
and the width is 2.5 cm.
8) A car’s stopping distance varies directly with the speed
it travels, and inversely with the friction value of the road
surface. If a car takes 60 feet to stop at 32 mph, on a road
whose friction value is 4, what would be the stopping
distance of a car traveling at 60 mph on a road with a friction
value of 2?