The difference between two numbers is 15
.
Three
times the larger number is eight
times the smaller. Find the two numbers.
Just translate from English to Math
larger number --- x
smaller number --- y
x-y = 15---> x = y + 15
3x = 8y
3(y+15) = 8y
3y + 45 = 8y
45 = 5y
y = 9 , then
x = 9+15 = 24
state your conclusion
Well, well, well! It seems we have a mathematical conundrum on our hands. Let's call the larger number "x" and the smaller number "y".
According to the problem, the difference between the two numbers is 15. So, we can write our first equation as:
x - y = 15
Now, the problem goes on to say that three times the larger number (3x) is eight times the smaller number (8y). So, our second equation can be written as:
3x = 8y
Now, it's time for a little substitution dance! We can solve one equation for one variable and substitute it into the other equation. Let's solve the first equation for x:
x = 15 + y
Now, we can substitute this expression for x into the second equation:
3(15 + y) = 8y
And now we can simplify and solve for y:
45 + 3y = 8y
5y = 45
y = 9
Now that we know the value of y, we can substitute it back into the first equation to find x:
x - 9 = 15
x = 24
So, the larger number is 24 and the smaller number is 9.
Voilà! The mystery of the two numbers has been solved, thanks to the power of mathematics and a little bit of clownery.
Let's assume the larger number as 'x' and the smaller number as 'y'.
According to the given information, the difference between the two numbers is 15, so we can write the equation:
x - y = 15 (Equation 1)
We are also given that three times the larger number is eight times the smaller number, so we can write:
3x = 8y (Equation 2)
Now, we can solve these two equations simultaneously to find the values of x and y.
To eliminate one variable, we can multiply Equation 1 by 3 and Equation 2 by 15:
3(x - y) = 3(15)
15x = 120y
Expanding these equations, we get:
3x - 3y = 45
15x = 120y
Rearranging Equation 2, we get:
120y = 15x
Now, we can equate the expressions for y in both equations:
3x - 3y = 45 (Equation 3)
15x = 120y (Equation 4)
-----------------
15x - 15y = 225 (Equation 5) (Multiplying Equation 3 by 5)
Now, we can subtract Equation 5 from Equation 4:
15x - 15y - (15x - 15y) = 225 - 15x
0 = 225 - 15x
15x = 225
x = 225 / 15
x = 15
Substituting the value of x in Equation 1, we can find y:
15 - y = 15
y = 15 - 15
y = 0
Therefore, the two numbers are 15 and 0.
To find the two numbers, we can set up a system of equations based on the given information. Let's call the larger number x and the smaller number y.
1) "The difference between two numbers is 15."
This can be expressed as: x - y = 15
2) "Three times the larger number is eight times the smaller."
This can be written as: 3x = 8y
Now we have a system of equations with two variables. We can solve them simultaneously to find the values of x and y.
We'll use the method of substitution to solve the system:
From equation 1, we have:
x - y = 15 ---> x = y + 15
Substitute this value of x into equation 2:
3(y + 15) = 8y
Simplify the equation:
3y + 45 = 8y
Move the variables to one side:
8y - 3y = 45
5y = 45
Solve for y:
y = 45 / 5
y = 9
Now substitute the value of y back into equation 1 to find x:
x = y + 15
x = 9 + 15
x = 24
Therefore, the two numbers are 24 and 9.
b-s = 15
3 b = 8 s
so b = 8s/3
8s/3 - 3s/3 = 15
5 s/3 = 15
s/3 = 3
s = 9
b = 9+15 = 24