let the smaller be x
then the larger is x+4
Now just translate
"sum of five times the smaller number and the bigger number is 58 "
---> 5x + x+4 = 58
solve for x
then the larger is x+4
Now just translate
"sum of five times the smaller number and the bigger number is 58 "
---> 5x + x+4 = 58
solve for x
We are given that the difference between the two numbers is 4, so we can write the equation:
y - x = 4 ----(Equation 1)
Additionally, we are given that the sum of five times the smaller number and the bigger number is 58. This can be written as the following equation:
5x + y = 58 ----(Equation 2)
Now, we have a system of two equations with two unknowns. We'll use these equations to find the values of x and y.
To solve the system, we can use the method of substitution or elimination. Let's use the substitution method:
From Equation 1, we can write y = x + 4.
Substituting this into Equation 2, we get:
5x + (x + 4) = 58
Combining like terms, we have:
6x + 4 = 58
Subtracting 4 from both sides, we get:
6x = 54
Dividing both sides by 6, we find:
x = 9
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
y = x + 4 = 9 + 4 = 13
Therefore, the smaller number is 9 and the bigger number is 13.