one number is four times the other and the difference between the two number is 21. Find the two numbers.
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Answers
Answer:
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Step-by-step explanation ; Let the numbers be x and y.
A number is 4 times another number,
x = 4y…Eq..1
if 21 is added to both the numbers then first number becomes 7/4 times the other number.
(x + 21)/(y + 21) = 7/4
Cross multiplication
4 (x + 21) = 7 (y + 21)
4x + 84 = 7y + 147
4x - 7y = 147 – 84
4x - 7y = 63…Eq..2
Now putting the value of x from Eq.1 to Eq..2
4 (4y) - 7y =63
16y – 7y = 63
9y = 63
y = 63/9
y = 7
One number is 7
To derive the other number, putting the value of y in Eq..1
x = 4y
x = 4 × 7
x = 28
The other number is 28
Thus the two numbers are 7 and 28 .Now Checking the correctness of answer by substituting the values of both numbers in the Eq..2
4x - 7y = 63
4 × 28 - 7 × 7 = 63
112 - 49 = 63
63 = 63
Means answer is correct.
Given :
one number is four times the other and the difference between the two number is 21
Solution
Let the first number = x
So,
The other number = 4x
4x - x = 21
3x = 21
x = 21/3
x = 7
The numbers = x & 4x
The numbers = 7 & 4×7
= 7 , 28
Hope this will help....