Question

What must be added to the numbers 8, 14, 28 and 42 so that they are in proportion?
(A) 3
(B) 7
(C) 9
(D) 8.
Explain the whole question.
​

Answer 1

Answer:

2 needs to be added to each of the 4 numbers - 6, 14, 18 and 38 to make the resulting numbers in proportion.

Step-by-step explanation:

✔️ Let us add x to each of the four numbers to get (6+x):(14+x)::(18+x):(38+x). The product of the ends = the product of the means, or

(6+x)(38+x) = (14+x)(18+x), or

x^2 + 44x + 228 = x^2 + 32x + 252, or

44x - 32x = 252–228, or

12x = 24, or x =2.

⏩Check:⤵️

8:16::20:40 or 8*40 = 320 same as 16*20 - 320. Correct.

⏩Hence⤵️

2 needs to be added to each of the 4 numbers - 6, 14, 18 and 38 to make the resulting numbers in proportion.

Answer 2

$\boxed{ \boxed{ \sf \red{Firstly \: let \: us \: understand}}}$

$\sf{Assume \: two \: ratios \: are \: in \: proportion \: i.e.}$

$\sf{ a:b :: c:d}$

$\sf{here : \: a \: \& \: d \: are \: called \:\red{product \: of \: extremes }} \\ \sf{ \: \: \: \: \: \: \: \: b \:\& \: c \: are \: called \: \red{product \: of \: means} }$

$\boxed{ \boxed{ \sf \red{ Let \: us \: come \: to \: question}}}$

What must be added to the numbers 8, 14, 28 and 42 so that they are in proportion ?

$\underline{ \underline{{ \sf \red{Answer}}}}$

$\sf \red{Given: }$

$\rm{\: numbers \: are : \: 8 ,\: 14, \: 2, \: 42 }$

$\rm{let \: the \: number \: x \: needs \: to \: be \: added}$

$\mathrm\red{adding \:x \: to \: the \: numbers \: we \: get : }$

$\rm{8 + x ,\: 14+ x ,\: 28 + x, \: 42 + x}$

$\sf\red{also \: given, \: the \: numbers \: are \: \: proportional}$

$\rm{8+ x : 14+ x : : 28 + x :42 + x }$

$\sf \red{now}$

$\boxed{ \boxed{ \sf \blue{products \: of \: means \: = \: product \: of \: extremes}}}$

$\rm{(14 + x )( 28 + x) = (8 + x)(42 + x)}$

$\rm{392 + 14x + 28x + {x}^{2} =336 + 8x + 42x + {x}^{2} }$

$\rm{ {x}^{2} +42x + 392 \: = \: {x}^{2} + 50x + 336 }$

$\rm{ {x}^{2} - {x}^{2} + 392 - 336 = 50x - 42x }$

$\rm{56 = 8x}$

$\rm{x \: = \: \frac{56}{8} }$

$\boxed{ \boxed{\rm{x = 7}}}$

so answer is x = 7