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The sum of three numbers is 106. The second number is 2 times the third. The first number is 6 more than the third. What are the numbers?First numberSecond number Third number

User CroaToa
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1 Answer

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19 votes

Let's call the numbers a, b and c.

The first statement tells us that the sum of the three numbers is 106, so:


a+b+c=106.

The second statement tells us that the second number is two times the third so:


b=2c\text{.}

The final statement tells us that the first number is 6 more than the third, so:


a=c+6.

This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:


(c+6)+b+c=106,
2c+b+6=106,
2c+b=100,
b=100-2c\text{.}

Let's take this value of b and use it in the second equation:


100-2c=2c,
100=4c,
c=25.

Now we know the exact value of c, so let's go back to the third equation:


a=25+6=31,

and now we also know the exact value of a, so let's go back to the second equation:


b=2(25)=50.

So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.

31+50+25=106.

User Mycoola
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