Question

A positive number is 5 times another number. If 21 is added to both the numbers,
then one of the new numbers becomes twice the other new number. What are the
numbers?

Answer 1

Answer:

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.

Answer 2

Answer:

Numbers- 7 and 35

Step-by-step explanation:

Let the number be 'X'

and another number be 'Y'

According to the question-

1st case

X=5Y......(1)

2nd case

X+21=2(Y+21)....(2)

by substituting the value of 'Y'

in EQ..(2)

we get,

5Y+ 21= 2(Y+21)

5Y+21=2Y+42

5Y-2Y =42-21

3Y=21

Y=21/3

Y=7

by putting the value of 'Y' in EQ ..(1)

we get X=5*7

X=35