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The sum of three numbers is 105. The third number is 9 more than the first. The second number is 4 times the third. What are the numbers?

User Metacubed
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1 Answer

4 votes

Answer:

First number = 10

Second number = 19

Third number = 76

Explanation:

This problem presents an equation of a sum of three terms which add up to 105, a + b + c = 105.

The unknown first number can be defined as an unknown variable x.

The third number is 9 more than the first, so we define it as x + 9.

The second number is 4 times the third term, so we define it as 4 * (x + 9). We can expand this term into 4 * x + 4 * 9 = 4x + 36.

Thus, the equation we are given is x + (4x + 36) + (x + 9) = 105.

Adding up like terms, we get 6x + 45 = 105.

Now, to solve for the unknown variable x, we need to isolate the variable on one side of the equation. First, we subtract 45 from both sides, 6x + 45 - 45 = 105 - 45, which yields 6x = 60. Then, we divide both sides by 6, 6x/6 = 60/6. This yields x = 10.

Now that we know the first number, we must find the third number by substituting it into the term, and we get (10) + 9 = 19.

We multiply the third term by four, and find that the second number is 4 * (19) = 76.

The first, second, and third numbers are 10, 19, and 76, respectively, and their sum is 10 + 19 + 76 = 105.

User Thorvald
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