QUESTION 4
Easy
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?
SOLUTION
1
Assume the numbers
Let the smaller number be \(x\). Then the bigger number must be \(5x\).
2
Add \(21\) to both the numbers, form the equation using the condition given, and solve for \(x\)
After adding \(21\) to both numbers, they become \(x + 21\) and \(5x + 21\).
The new bigger number is twice the new smaller, i.e.,
\(5x + 21 = 2(x + 21)\)
⇒ \(5x + 21 = 2x + 42\)
⇒ \(5x − 2x = 42 − 21\)
⇒ \(3x = 21\)
⇒ \(x = 7\)
The new bigger number is twice the new smaller, i.e.,
\(5x + 21 = 2(x + 21)\)
⇒ \(5x + 21 = 2x + 42\)
⇒ \(5x − 2x = 42 − 21\)
⇒ \(3x = 21\)
⇒ \(x = 7\)
3
Write down the two numbers
Smaller number = \(x = 7\)
Bigger number = \(5x = 5(7) = 35\)
Bigger number = \(5x = 5(7) = 35\)
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Final Answer : The numbers are \(7\) and \(35\).
Concept Note
Use ratio \(1:5\) to express the numbers as \(x\) and \(5x\). Set up the equation using conditions given in the question and solve.