Question

One number, y, is 5 less than 3 times another number, x. The sum of the numbers is 30. If x and y are the two numbers, which system of equations that can be used to find their values.

Answer 1

The system of equations to solve the given problem is y = 3x - 5 and x + y = 30. By solving these linear equations, we find that the two numbers are x = 8.75 and y = 21.25.

Step-by-step explanation:

To solve the mathematical problem presented by the student, we must set up a system of linear equations that reflects the conditions given in the problem statement. The first condition provided is that one number, y, is 5 less than 3 times another number, x. This can be expressed by the equation y = 3x - 5. The second condition states that the sum of the numbers is 30, which gives us the equation x + y = 30. To solve the system of equations, we have:

1. y = 3x - 5
2. x + y = 30

Now, we can use the substitution method to solve for one variable. We can substitute the expression for y from the first equation into the second equation:

x + (3x - 5) = 30

Now we see that:

1. 4x - 5 = 30
2. 4x = 35
3. x = 8.75

Having found the value of x, we can substitute it back into the first equation to find y:

y = 3(8.75) - 5

y = 26.25 - 5

y = 21.25

Therefore, the values of x and y that satisfy the system of equations are 8.75 and 21.25, respectively.