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If x is inversely proportional to y, and y = 5 when x = 2, find the value of x, when y = 41.
4211тАЛ
4110тАЛ
4210тАЛ
4412тАЛ
4110тАЛ
Since x is inversely proportional to y, the product xy remains constant. Calculate constant k = 2 * 5 = 10. Then x = 10 / 41.
x is inversely proportional to y. y = 5 when x = 2. Find x when y = 41.
xтИЭy1тАЛтЯ╣x=ykтАЛтЯ╣xy=k
Since x is inversely proportional to y, the product xy remains constant. Calculate constant k = 2 * 5 = 10. Then x = 10 / 41.
Students often mistake inverse proportion for direct proportion (x = ky), leading to x = 2 * (41/5) = 16.4 instead of the correct inverse value.
Define the relationship
Since x is inversely proportional to y, the product of x and y is constant: x├Чy=k
x├Чy=k
Calculate the constant k
Using the given values x = 2 and y = 5: k=2├Ч5=10
k=10
Solve for x
Substitute k = 10 and y = 41 into the equation x=ykтАЛ:
x=4110тАЛ
B is correct because the constant product of the variables is 10, resulting in x = 10/41 when y = 41.
This concept is foundational for 'Work and Time' problems where speed is inversely proportional to time taken for a fixed distance.
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