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If the fourth proportional to 2x, 3x, and 12 is y, find y.
16
18
24
20
18
Use the property that the product of extremes equals the product of means: (First├ЧFourth)=(Second├ЧThird). Here, (2x├Чy)=(3x├Ч12).
The first, second, and third terms of a proportion are 2x, 3x, and 12, respectively. The fourth proportional is y.
baтАЛ=dcтАЛ
Use the property that the product of extremes equals the product of means: (First├ЧFourth)=(Second├ЧThird). Here, (2x├Чy)=(3x├Ч12).
Students often fail to cancel out the variable x on both sides, leading to confusion or incorrect expressions involving x in the final answer.
Set up the proportion
Since y is the fourth proportional to 2x, 3x, and 12, we can express the relationship as a ratio equality.
3x2xтАЛ=y12тАЛ
Simplify the ratios
Cancel the x term from the left side fraction.
32тАЛ=y12тАЛ
Solve for y
Cross-multiply to isolate y: 2y=3├Ч12, which gives 2y=36. Dividing by 2 yields y.
y=236тАЛ=18
B is correct because the calculation y=18 satisfies the proportion relationship for the given terms.
This concept of fourth proportionals is foundational for understanding 'Variation' (Direct/Inverse), which is frequently tested in speed-time-distance problems.