The sum of three numbers is 113. The second number is 3 times the third. The first number is 7 less than the third. What are the numbers?

number 1 = 17 number 2 = 72 number 3 = 24
work:
the three numbers are symbolized as x, y, and z
x + y + z = 113
number 2 (y) is 3 times the third number (z) so
y = 3z
so x + 3z + z = 113
the first number (x) is 7 less than than the third number (z) so
x = z - 7
so z -7 + 3z + z = 113
5z - 7 = 113 5z = 120
z = 24
x = 17 **y = 72
Hope this helped :) **

Answered by YanaMyles | 2024-06-24

The problem is a simple system of equations in mathematics, and by defining variables and combining like terms, the solution is that the three numbers are 17, 72, and 24.
The student is asked to solve a system of equations where the sum of three numbers is 113, the second number is 3 times the third, and the first number is 7 less than the third. To find these numbers, we need to set up a system of linear equations based on the information provided:

Let the third number be x.
According to the problem, the second number is 3 times the third, so it can be represented as 3x.
The first number is 7 less than the third, so it can be represented as x





Together, their sum equals to 113, which gives us the equation x + 3x + (x - 7) = 113.

Combining like terms in the equation above, we get 5x - 7 = 113. Adding 7 to both sides, we have 5x = 120. Finally, dividing both sides by 5, we find x = 24.
With x now known, we can calculate the first number as x - 7, which is 17, and the second number as 3x, which is 72. Therefore, the three numbers are 17, 72, and 24 respectively.

Answered by SravyaDa | 2024-06-25

The three numbers are 17, 72, and 24, where the first number is 17, the second number is 72 (3 times the third), and the third number is 24. The system of equations was solved to find these values. By setting up the equations based on the problem's conditions, we determined the values accordingly.
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Answered by YanaMyles | 2024-10-01