The second of two numbers is 6 times the first. Their sum is 77. Find the numbers.
6x + x = 77
7x = 77
x = 11
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To solve this problem, we can set up a system of equations:
Let's say the first number is x.
The second number is then 6 times the first, which is 6x.
According to the problem, the sum of the two numbers is 77:
x + 6x = 77
Combine like terms:
7x = 77
Divide both sides by 7 to isolate x:
x = 11
So, the first number, x, is 11.
To find the second number, multiply the first number by 6:
6x = 6 * 11 = 66
Therefore, the second number is 66.
In conclusion, the first number is 11, and the second number is 66.