Question
The difference between two numbers is $7$. Six times the smaller plus the larger is $77$. Find the numbers.
✓
Answer
Let the smaller number be $‘x’$.So, the larger number $= x + 7$.
According to question:
$6x + (x + 7) = 77$
$6x + x + 7 = 77$
$7x + 7 = 77$
Subtracting $7$ from both sides, we get
$7x + 7 - 7 = 77 - 7$
$7x = 70$
Dividing both sides by $7$, we get
$\frac{7\text{x}}{7}=\frac{70}{7}$
$\text{x}=10$
Thus, the smaller number $= x = 10,$ and the larger number $= x + 7 = 10 + 7 = 17.$
The two required numbers are $10$ and $17$.
According to question:
$6x + (x + 7) = 77$
$6x + x + 7 = 77$
$7x + 7 = 77$
Subtracting $7$ from both sides, we get
$7x + 7 - 7 = 77 - 7$
$7x = 70$
Dividing both sides by $7$, we get
$\frac{7\text{x}}{7}=\frac{70}{7}$
$\text{x}=10$
Thus, the smaller number $= x = 10,$ and the larger number $= x + 7 = 10 + 7 = 17.$
The two required numbers are $10$ and $17$.
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