QUESTION 4
Easy
The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.
SOLUTION
1
Use the ratio given in the question to express the integers
Let the two positive integers be \(2k \) and \(5k\), where k is a positive number.
2
Write their difference to form the equation
\(5k − 2k = 63\)
3
Simplify and solve for \(k\)
\(3k = 63\)
⇒ \( k = 21\)
⇒ \( k = 21\)
4
Find the integers
first integer = \(2k = 2(21) = 42\)
second integer = \(5k = 5(21) = 105 \)
second integer = \(5k = 5(21) = 105 \)
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Final Answer : The two integers are 45 and 105.
Concept Note
To find the two integers, use the ratio \(a:b\) to write the numbers as \(ak\) and \(bk\). Form an equation from their difference, solve for \(k\), and then find the integers.