The sum of two numbers is 33. The sum of the smaller and 3 times the larger is 81. Find the numbers.
x+ y = 33
x + 3y = 81
Subtract first equation from second.
2y = 48
Take it from here.
Ah, numbers and their mathematical dramas! Let's give this puzzle a whirl.
Let's say the smaller number is "x" and the larger number is "y." According to the problem, we have two equations to work with:
1) x + y = 33
2) x + 3y = 81
Now let's have a little fun with clown logic to solve these equations.
To eliminate x, let's subtract Equation 1 from Equation 2 (because we all know clowns love to subtract):
2) x + 3y = 81
- 1) x + y = 33
If we do the math, my wacky friend, we get:
2y = 48
Now it's time for some division madness! We'll divide both sides of the equation by 2 (clowns never miss a chance to divide things!):
y = 24
So we found that the larger number is 24. But wait, there's more!
We can now substitute this value back into Equation 1 to find the smaller number (clowny math at its finest):
x + 24 = 33
By subtracting 24 from both sides (more clown subtraction!):
x = 9
So the smaller number is 9.
To recap, the smaller number is 9 and the larger number is 24. Ta-da!
Let's assume the smaller number is x and the larger number is y.
According to the problem, we have two equations:
1. x + y = 33 (the sum of two numbers is 33)
2. x + 3y = 81 (the sum of the smaller and 3 times the larger is 81)
To solve these equations, we can use the method of substitution or elimination.
Let's solve the first equation for x:
x = 33 - y
Now substitute this value of x into the second equation:
(33 - y) + 3y = 81
Simplifying the equation:
33 - y + 3y = 81
33 + 2y = 81
2y = 81 - 33
2y = 48
y = 48 / 2
y = 24
Now substitute this value of y into the first equation to find x:
x + 24 = 33
x = 33 - 24
x = 9
Therefore, the smaller number is 9 and the larger number is 24.
To solve this problem, let's assume the smaller number as 'x' and the larger number as 'y'. We are given two pieces of information:
1. The sum of the two numbers is 33: x + y = 33.
2. The sum of the smaller number and 3 times the larger number is 81: x + 3y = 81.
Now we need to solve this system of equations to find the values of x and y.
There are multiple ways to solve these equations, but let's use the substitution method.
Step 1: Solve the first equation for x:
x = 33 - y
Step 2: Substitute this value of x into the second equation:
33 - y + 3y = 81
Step 3: Simplify and solve for y:
2y = 48
y = 24
Step 4: Substitute the value of y back into the first equation to find x:
x + 24 = 33
x = 9
So the smaller number is 9, and the larger number is 24.