A positive number is 5 times the other 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
Answers
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Question
A positive number is 5 times the other 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?
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Answer
Let the first number be 'x'
The second number would be '5x'
According to the question, we'll add 21 to both numbers.
x + 21 and 5x + 21 will be the numbers obtained.
As the question says,
⇒ 2 (x + 21) = 5x + 21
Let's solve the equation step-by-step.
2 (x + 21) = 5x + 21
Step 1: Simply the equation.
⇒ 2 (x + 21) = 5x + 21
⇒ 2x + 42 = 5x + 21
Step 3: Subtract 21 from both sides of the equation.
⇒ 2x + 42 - 21 = 5x + 21 - 21
⇒ 2x + 21 = 5x
Step 4: Flip the equation.
⇒ 2x + 21 = 5x
⇒ 5x = 2x + 21
Step 5: Subtract 2x from both sides of the equation.
⇒ 5x - 2x = 2x + 21 - 2x
⇒ 3x = 21
Step 6: Divide 2 from both sides of the equation.
⇒ 3x ÷ 3 = 21 ÷ 3
⇒ x = 7
∴ x = 7 in the formed equation.
∴ Smaller number = x = 7
∴ Greater number = 5x = 5 × 7 = 35
∴ The required numbers are 7 and 35.
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