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If 5 + x, 2x + 7, 6x + 9, and y are in proportion when x = 2, find the value of y.
Question

If 5 + x, 2x + 7, 6x + 9, and y are in proportion when x = 2, find the value of y.

A.

33

B.

28

C.

42

D.

45

Correct option is A

Given:
Four terms 5 + x, 2x + 7, 6x + 9, and y are in proportion.
Value of x = 2.
Concept Used:
If four terms a, b, c, and d are in proportion, then:
​ab=cd\frac{a}{b} = \frac{c}{d}​​
which implies a⋅d=b⋅ca \cdot d = b \cdot c​​
Solution:
Terms are in proportion, so;
​5+x2x+7=6x+9y\frac{5+x}{2x + 7} = \frac{6x + 9}{y}​​
Putting x = 2 ,
​5+22×2+7=6×2+9y\frac{5+2}{2 \times 2+7} = \frac{6 \times 2+9}{y}​​
​711=21y\frac{7}{11} = \frac{21}{y}​​
​ ⟹ y=21×117=33\implies y = \frac{ 21 \times 11}{7}= 33​​
Thus, the value of y is 33.

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