SOLUTION: Please solve this equation:The mass of rice that each woman gets when sharing a sack varies inversely with the number of women.When there are 20 women,each gets 6kg of rice.If ther

Question 1022430: Please solve this equation:The mass of rice that each woman gets when sharing a sack varies inversely with the number of women.When there are 20 women,each gets 6kg of rice.If there are nine women,how much does each get?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for inverse variation is y = k/x.

let y = the amount of rice each woman gets.
let x = the number of women.

when y = 6 and x = 20, the formula becomes 6 = k/20.

solve for k to get k = 120.

when the number of women becomes 9 and k = 120, then the formula of y = k/x becomes y = 120/9 which results in y = 13 and 1/3.

the constant of variation here is the amount of rice in the bag.
as long as that doesn't change, then the constant of variation remains the same for all of the similar equations involving it.

for example:

you have 120 kilograms of rice total.
divide that by 20 women and each gets 6 kilograms of rice.

divide the same 120 kilograms of rice total by 9 women and each gets 13 and 1/3 kilograms of rice.

each woman gets 13 and 1/3 kilograms of rice.

9 * 13 and 1/3 equals 117 + 3 equals 120 kilograms of rice total.

numbers check out so your solution is each woman gets 13 and 1/3 kilograms of rice when the number of women becomes 9.

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