the sum of two numbers is 80.if the larger number exceeds four times the smaller one by 5.the number is
work
x+y=80, 4x-y=5
Nope: y = 4x+5
20
10
To solve this problem, we can use a system of equations. Let's assign variables to the given information:
Let x be the larger number.
Let y be the smaller number.
From the given information, we can form two equations:
Equation 1:
The sum of the two numbers is 80, so x + y = 80.
Equation 2:
The larger number (x) exceeds four times the smaller number (y) by 5, so 4y + 5 = x.
Now, we have a system of equations:
Equation 1: x + y = 80
Equation 2: 4y + 5 = x
To solve the system, we can use the substitution method or the elimination method.
Let's use the substitution method:
From Equation 1, we can solve for x:
x = 80 - y
Now, we substitute the value of x in Equation 2:
4y + 5 = 80 - y
Adding y to both sides:
5y + 5 = 80
Subtracting 5 from both sides:
5y = 75
Dividing both sides by 5:
y = 15
Now, we substitute the value of y back into Equation 1 to solve for x:
x + 15 = 80
Subtracting 15 from both sides:
x = 65
Therefore, the larger number is 65 and the smaller number is 15.