The difference between two numbers is 4.If the sum of five times the smaller number and the bigger number is 58, what are the numbers?
To solve this problem, let's assume the smaller number is x and the bigger number is y.
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.
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