Final answer:
The two numbers that satisfy the given conditions are 24 and 34. A system of equations was set up and solved using substitution to find the figures.
Step-by-step explanation:
To find the two numbers, we need to set up a system of equations based on the information given. The sum of two numbers is 58, so we have:
Equation 1: x + y = 58
Twice the second number subtracted from four times the first number is 28, which gives us:
Equation 2: 4x - 2y = 28
We can now solve this system of equations by using the substitution or elimination method. Let's use the substitution method by solving equation 1 for y:
y = 58 - x
Next, we substitute the expression for y into equation 2:
4x - 2(58 - x) = 28
Expanding and simplifying gives us:
4x - 116 + 2x = 28
6x = 144
x = 24
Now, we substitute x back into equation 1 to find y:
24 + y = 58
y = 34
Therefore, the two numbers are 24 and 34.