Question

The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers. [2 Marks]

Answer 1

Let the smaller number be ‘x’.
So, the larger number = x + 7.
According to the question:
$\Rightarrow 6x+(x+7)=77$
$\Rightarrow 6x+x+7=77$
On simplifying we get
$7x+7=77$
Subtracting 7 from both sides, we get
$\Rightarrow 7x+7–7=77–7$
$\Rightarrow 7x=70$
Dividing both sides by 7, we get
$\Rightarrow \frac{7x}{7}=\frac{70}{7}$
$\Rightarrow x=10$
Thus, the smaller number = x = 10 [1 Mark]
And the larger number = x + 7 = 10 + 7 = 17.
The two required numbers are 10 and 17. [1 Mark]