Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 4

8 / 11

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Answer

1
Since the ratio of the two integers is 2:5, express them in terms of a common factor x.
Let the two integers be $2x$ and $5x$
2
Use the given difference between the two integers to find x.
\text{$5x - 2x = 63$ $\quad$ ${color:#625b5f}[The difference between the integers is 63]{/color}$}
⇒
$3x = 63$
⇒
\text{ $x = \dfrac{63}{3}$}
⇒
$x = 21$
3
Substitute x = 21 to find the two integers.
\text{$2x = 2 × {color:#2E2EFF}21{/color} = 42$ $\quad$ ${color:#625b5f}[First integer]{/color}$}
\text{$5x = 5 × {color:#2E2EFF}21{/color} = 105$ $\quad$ ${color:#625b5f}[Second integer]{/color}$}
4
Write the two integers.
Answer: The two integers are 42 and 105.
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