Variation Word Problems
The total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing. If a gallon of gas cost $2.25, then how many gallons could you purchase for $18?
8 gallons
If y varies directly as x, and y = 3 when x = 9, find x when y = 5.
15
What is the common difference of the following sequence: 1,3,5,7...
2
Given: 72, 12, 2... Find the common ratio
1/6
S20 for the geometric series 2+4+8+16+…
2,097,150
The number of calories in a hamburger varies directly with the hamburger's weight. If a quarter-pound burger has 560 calories, how many calories does a half-pound hamburger have?
1120 calories
If y varies inversely as x, and y = 39 when x = 3, find y when x = 11. (no decimals)
117/11
Given 8,15,22,... Write the explicit formula. (Write the rule)
What is an=7n+1
Find the explicit formula (write the rule) for the following sequence:
25, 5, 1, 1/5, ....
=25(1/5)^(n-1)
Find the sum of the first 11 terms
6, 7.4, 8.8...;
143
On a map, distance in km and distance in cm varies directly, and 25 km are represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance between them?
87.5 km
Y varies Jointly as X and Z. Find Y for the given values of X and Z. Y=-108 when X=-4 and Z=3; X=6 and Z=-2
Y=-108
Given: 7,13,19,...find a12
73
This is the explicit formula for the geometric sequence -5, 10, -20, 40, ...
a_n=-5*(-2)^(n-1)
Find S98 for the following series:
0.2, 0.4, 0.6, ...
970.2
The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.
50 ohms
Z varies directly with W and inversely with X. Find Z for the given values of X and W. Z=2 when X=4, W=8; X=8,W=2
1/4
a25=79 a9=31, write the rule
an=3n+4
Find the 10th term of the sequence:
-3, 6, -12, 24, ....
a10= 1536
Susan got a new job and earned $1 the first day, $2 the 2nd day, $4 the 3rd day and so on. How much will she have earned after 10 days?
$1023
The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 230 cubic centimeters when the temperature is 400 degrees and the pressure is 20 pounds per square centimeter, what is the volume when the temperature is 270 degrees and the pressure is 30 pounds per square centimeter?
103.5 cubic centimeters
Z varies directly with X and inversely with the square of W. Find Z for the given values of X and W. Z=5 when X=4, W=10; X=2,W=5
10
a8=-6 a34=7, a50=?
15
a10 =?
3, 12, 48, 192, ...
786, 432
Find the sum of the infinite geometric series:
2/3+4/9+8/27...
2