The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers.
Please help. ^.^
x+y=15
3x = 5y-11
3x = 5(15-x)-11
3x = 75-5x-11
8x = 64
x=8
y=7
Why am i here i need help
Why did the mathematician get stuck with this problem? Because it was a real "sum-oh!" situation!
Okay, let's tackle this math jest! Let's call the two numbers x and y (aren't they lucky to get such fancy names?). From the problem, we know that:
x + y = 15 (Sum of two numbers is 15)
And we also know that:
3x = 5y - 11 (Three times one number is 11 less than five times the other)
Now, we can solve these equations using some good old-fashioned math humor!
First, let's isolate a variable (y) in one of the equations. Let's use the first equation:
x + y = 15
If we subtract x from both sides, we get:
y = 15 - x
Now, we can substitute this expression for y in the second equation:
3x = 5(15 - x) - 11
Multiply the 5 by everything in the parentheses:
3x = 75 - 5x - 11
Combine like terms:
8x = 64
Divide by 8 on both sides:
x = 8
Now we know one of the numbers! Let's substitute this value back into the first equation:
8 + y = 15
Subtract 8 from both sides:
y = 15 - 8
y = 7
And there you have it! The two numbers are x = 8 and y = 7. Keep those numbers handy, you never know when they might come in handy for a math joke!
To find the numbers, let's assign variables to represent them. Let's call one of the numbers "x" and the other number "y".
Given that the sum of the two numbers is 15, we can write the equation:
x + y = 15 (equation 1)
Now let's use the second piece of information. It states that three times one of the numbers is 11 less than five times the other. We can translate this into an equation as follows:
3x = 5y - 11 (equation 2)
We now have a system of two equations (equation 1 and equation 2) that we can solve simultaneously to find the values of x and y.
To do this, we can use the method of substitution or elimination. Let's use substitution:
From equation 1, we can isolate x:
x = 15 - y
Now substitute this expression for x in equation 2:
3(15 - y) = 5y - 11
Distribute the 3:
45 - 3y = 5y - 11
Next, simplify the equation by combining like terms:
-3y - 5y = -11 - 45
-8y = -56
Divide both sides of the equation by -8 to solve for y:
y = -56 / -8
y = 7
Now substitute this value of y back into equation 1 to solve for x:
x + 7 = 15
x = 15 - 7
x = 8
Therefore, the two numbers are x = 8 and y = 7.
So, the numbers are 8 and 7.