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If x varies directly as y and x = 10 when y = 5, what is x when y = 15?
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30
Observe the change in y: y increased from 5 to 15, which is a factor of 3 (15/5=3). Since x is directly proportional, simply multiply the original x by the same factor: 10├Ч3=30.
x varies directly as y, where x = 10 when y = 5. Find x when y = 15.
y1тАЛx1тАЛтАЛ=y2тАЛx2тАЛтАЛ
Observe the change in y: y increased from 5 to 15, which is a factor of 3 (15/5=3). Since x is directly proportional, simply multiply the original x by the same factor: 10├Ч3=30.
Students often mistakenly apply an inverse variation formula (x1тАЛy1тАЛ=x2тАЛy2тАЛ) instead of direct variation, leading to the incorrect answer of 10/3.
Define the relationship
Since x varies directly as y, we express the relationship as x=ky, where k is the constant of variation.
x=ky
Calculate the constant k
Substitute the given values x=10 and y=5 to find k.
10=k├Ч5тЯ╣k=510тАЛ=2
Find x for new y
Using the constant k=2 and the new value y=15, calculate the new x.
x=2├Ч15=30
C is correct because applying the direct variation principle with a constant of 2 leads to a value of 30 when y is 15.
Direct variation is the fundamental concept behind unitary method problems and speed-distance-time relations where one variable is held constant.
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