A positive number is five times another number if 21 is added to both the numbers then one of the new number becomes twice the other new number what are the numbers
Answers
Answer:
Step-by-step explanation:Let x be the first number and let y be the second number. From the first statement, we have:
x = 5y.
From the second statement, we have:
x + 21 = 2*(y + 21).
[Since x = 5y, x must be greater than y, so x + 21 must be greater than y+ 21. That's how we know x + 21 = 2*(y + 21), rather than the other way around, y + 21 = 2*(x + 21).]
So all we have to do is solve this system of equations. This can be done easily by substitution, since the first equation is already solved for x. Plugging in 5y for x in the second equation, we have:
5y + 21 = 2*(y + 21)
5y + 21 = 2y + 42
Distributing on the right-hand side
3y + 21 = 42
Subtracting 2y from both sides
3y = 21
Subtracting 21 from both sides
y = 7
Dividing both sides by 7
Thus, y = 7 and x = 5y = 5*7 = 35, so the two numbers are 7 and 35.