the sum of two number is 40. when 3¼ times the larger number is subtracted from 5½ times the smaller, the difference is -25. find the two numbers
Let's use algebra to solve this problem step-by-step.
Let's assume the larger number is x, and the smaller number is y.
From the given information, we have two equations:
1) x + y = 40 (the sum of the two numbers is 40)
2) 5.5y - 3.25x = -25 (when 3¼ times the larger number is subtracted from 5½ times the smaller, the difference is -25)
To solve the system of equations, we can use the method of substitution or elimination.
Let's solve using substitution:
From equation 1), we can isolate x: x = 40 - y
Now substitute this value of x into equation 2):
5.5y - 3.25(40 - y) = -25
Expanding, we get:
5.5y - 130 + 3.25y = -25
Combine like terms:
8.75y - 130 = -25
Add 130 to both sides:
8.75y = 105
Now divide both sides by 8.75:
y = 105 / 8.75
y ≈ 12
Now substitute this value of y back into the original equation to find x:
x + 12 = 40
Subtract 12 from both sides:
x = 28
So, the larger number is approximately 28, and the smaller number is approximately 12.
n + m = 40 ...13 n + 13 m = 520
11/2 n - 13/4 m = -25 ... 22 n - 13 m =-100
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the larger number is represented by 'x' and the smaller number is represented by 'y'.
From the information given, we can set up two equations:
Equation 1: x + y = 40 (the sum of the two numbers is 40)
Equation 2: 5.5y - 3.25x = -25 (3¼ times the larger number subtracted from 5½ times the smaller gives a difference of -25)
Now, we can use these equations to solve for the values of x and y.
One way to solve this system of equations is by substitution. Let's solve Equation 1 for x:
x = 40 - y
Now, we'll substitute this expression for x into Equation 2:
5.5y - 3.25(40 - y) = -25
Simplifying this equation:
5.5y - 130 + 3.25y = -25
8.75y - 130 = -25
8.75y = 105
y = 105 / 8.75
y ≈ 12
Now that we have the value of y ≈ 12, we can substitute it back into Equation 1 to solve for x:
x + 12 = 40
x = 40 - 12
x = 28
Therefore, the two numbers are x = 28 and y = 12.
Let's the be x, while the smaller be c
x+y=40
5.5y-3.25=-25
5.5y-3.25=(40-y)=-27
5.5y-130-3.25y=-27
5.5y-3.25y=-27+130
8.75y=105
y=105/8.75
y=12
c+12=40
c=40-12
c=28