The difference between two numbers is 86. Seven times the smaller is equal to 4 more than the larger. What are the numbers?
15 and 101
X = Larger number.
Y = Smaller number.
Eq1: X-Y = 86.
x = y+86.
7y = x + 4.
Eq2: x - 7y = -4.
In Eq2, replace X with y+86:
y+86 - 7y = -4.
-6y = -90.
Y = 15.
x-15 = 86.
X = 101.
Let's call the smaller number "x" and the larger number "y".
From the problem statement, we know that the difference between the two numbers is 86. This can be written as:
y - x = 86
Also, seven times the smaller number is equal to 4 more than the larger number, which can be written as:
7x = y + 4
Now we have a system of two equations:
1) y - x = 86
2) 7x = y + 4
To solve this system, we can use the substitution method. From equation 2), we can express y in terms of x:
y = 7x - 4
Substituting this expression for y in equation 1), we get:
7x - 4 - x = 86
6x - 4 = 86
6x = 90
x = 15
Now substitute the value of x back into equation 2):
7(15) = y + 4
105 = y + 4
y = 101
Therefore, the smaller number is 15 and the larger number is 101.
To solve this problem, let's break it down step by step.
Step 1: Define variables
Let's assume that the smaller number is "x", and the larger number is "y".
Step 2: Set up equations
According to the given information, we can set up two equations:
Equation 1: y - x = 86 (The difference between the two numbers is 86)
Equation 2: 7x = y + 4 (Seven times the smaller number is equal to 4 more than the larger number)
Step 3: Solve the equations
We can solve these equations using various methods such as substitution or elimination. Let's solve by substitution.
From Equation 1, we can rewrite it to y = x + 86.
Substituting this value of y into Equation 2, we get:
7x = (x + 86) + 4
Simplifying the equation, we have:
7x = x + 90
Subtracting x from both sides, we get:
6x = 90
Dividing both sides by 6, we find:
x = 15
Step 4: Find the other number
Now that we have the value of x, we can substitute it into Equation 1 to find y:
y - 15 = 86
y = 86 + 15
y = 101
Step 5: Conclusion
Therefore, the smaller number is 15, and the larger number is 101.