what number must be subtracted from each of the number 31,19,13,10 so that they are in proportion
Answers
Answer:
This attachment is the answer.
The number that must be subtracted from each number is 7.
Given,
The numbers = 31,19,13,and 10.
To Find,
The number.
Solution,
We will use the proportions formula in this question to find the number.
Before solving the question, we must understand the concept of extreme and mean in the proportions.
Extreme:- If a proportion is written in ratio form using a colon, the extremes are the values that are furthest apart.
For example:- p : q :: r : s. In this, 'p' and 's' is the extreme of proportions.
Mean:- In proportions, the means are the values associated with the middle terms.
For example:- p : q :: r : s. In this, 'q' and 'r' is the mean of proportions.
The formula of Proportions:
Product of extreme = product of mean.
⇒ p × s = q × r.
Let the number to be subtracted be 'x.'
Then,
(31-x) : (19-x) :: (13-x) : (10-x)
Now, we will use the formula,
⇒ p × s = q × r.
⇒ (31-x) × (10-x) = (19-x) × (13-x)
On multiplying,
⇒ 310 - 31x - 10x +x² = 247 - 13x -19x + x²
On eliminating x², we get
⇒ 310 - 41x = 247 - 32x
⇒ 310 - 247 = 41x - 32x
⇒ 63 = 9x
⇒9x = 63
On dividing, we get the value of x,
⇒ x = 7.
The number that must be subtracted from each number is 7.
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