Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 4

5 / 26

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
Let the smaller number be y. Express the larger number in terms of y.
Smaller number = $y$. So, larger number = $5y$
2
Form an equation using the condition that the larger new number is twice the smaller new number.
\text{5y + 21 = 2(y + 21) $\quad$ ${color:#625B5F}[The larger new number is twice the smaller new number.]{/color}$}
3
Solve the equation for y.
$5y + 21 = 2y + 42$
⇒
$5y - 2y = 42 - 21$
⇒
$3y = 21$
⇒
\text{ $y = \dfrac{21}{3}$}
⇒
$y = 7$
4
Substitute the value of y to find the larger number.
\text{$5y = 5 × 7 = 35$ $\quad$ ${color:#625B5F}[The larger number is 5y]{/color}$}
5
Write the two numbers.
Answer: The numbers are 7 and 35
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