the difference between 2 numbers is 40? they are in the ratio
9:7. What are the numbers ?
let the two numbers be 9x and 7x
9x - 7x = 40
x = 20
one number is 9(20) or 180 , the other is 140
check:
is 180:140 = 9:7
is 180 - 140 = 40 , YES
Well, let's use some mathematical clowning to figure this out!
If the difference between two numbers is 40, we can call the larger number "L" and the smaller number "S".
Now, according to the ratio 9:7, we can set up the equation:
L - S = 40
But wait, let's put on our funny hats and make things interesting!
To keep things in line with the ratio, let's introduce a clown variable "C" and multiply it with both numbers:
9C - 7C = 40
Now, this may sound like a circus act, but we need to solve for C.
9C - 7C = 40
2C = 40
C = 20
Okay, now we can go back and find the numbers L and S by multiplying 20 with the ratio:
L = 9C = 9 * 20 = 180
S = 7C = 7 * 20 = 140
So, the numbers are 180 and 140. Ta-da!
To find the two numbers, we can use the information provided:
Step 1: Set up the ratio equation based on the given information. The ratio of the two numbers is given as 9:7.
Step 2: Assign variables to the numbers. Let's say the smaller number is represented by x, and the larger number is represented by y.
Step 3: Write the ratio equation. According to the given information, the difference between the two numbers is 40. So we can set up the equation: y - x = 40.
Step 4: Set up a second equation using the ratio. The ratio between the two numbers is given as 9:7, so we can set up the equation: y = (9/7)x.
Step 5: Substitute the value of y from the second equation into the first equation: (9/7)x - x = 40.
Step 6: Simplify the equation: (9x - 7x) / 7 = 40.
Step 7: Combine like terms: 2x / 7 = 40.
Step 8: Multiply both sides of the equation by 7 to isolate the variable: 2x = 40 * 7.
Step 9: Simplify: 2x = 280.
Step 10: Divide both sides of the equation by 2 to solve for x: x = 280 / 2 = 140.
Step 11: Now that we have the value of x, we can substitute it into the second equation to find the value of y using the ratio equation. y = (9/7)x = (9/7) * 140 = 180.
Therefore, the two numbers are 140 and 180.
To find the numbers, we need to set up an equation based on the information given. Let's call the larger number "x" and the smaller number "y".
According to the given information, the difference between the two numbers is 40, so we can express this as:
x - y = 40 ----(Equation 1)
We are also given that the numbers are in the ratio of 9:7, which means the larger number is 9 times the smaller number:
x/y = 9/7 ----(Equation 2)
To solve the system of equations (Equation 1 and Equation 2), we can use substitution or elimination method.
Let's solve by substitution method:
From Equation 2, we can express x in terms of y:
x = (9/7)y
Now we substitute this expression for x in Equation 1:
(9/7)y - y = 40
Multiplying both sides by 7 to remove the fraction:
9y - 7y = 7(40)
2y = 280
Dividing both sides by 2:
y = 140
Now we substitute the value of y back into Equation 2 to find x:
x/y = 9/7
x/140 = 9/7
Cross-multiplying:
7x = 9 * 140
7x = 1260
Dividing both sides by 7:
x = 180
Therefore, the smaller number is 140 and the larger number is 180.