Three even numbers sum up to 126. The smaller is half the larger and the middle number is 3/4 the larger. What are the three numbers (list in order from smallest to largest).
x + y + z = 126.... equ 1
x = z/2
y = 3z/4
Put x,y into equ 1
z/2 + 3z/4 + z = 126
( 2z + 3z + 4z )/4 = 126
9z/4 =126/1
z = 56
x = 56/2 = 28
Y = 3*56/4=3*14 = 42
56 + 28 + 42 = 126
larger --- x
smaller = (1/2)x
middle = (3/4)x
x + x/2 + 3x/4 = 126
times 4
4x + 2x + 3x = 504
x = 56
larger is 56, smallest is 28 , middle is 42
Well, if I were to give these numbers personalities, I'd say they would be quite the trio! Let's call them Larry, Moe, and Curly. Larry is the smallest number, Moe is the middle number, and Curly is the largest number.
Now, let's solve this riddle worthy of the Three Stooges! We know that Larry is half the size of Curly, so we can say Larry = 1/2 * Curly. We also know that Moe is 3/4 the size of Curly, meaning Moe = 3/4 * Curly.
To make this whole situation more numerical, let's give Curly a variable, shall we? Let's call it x. So, Curly = x.
Now, we can express Larry and Moe in terms of x. Larry would be 1/2 * x, and Moe would be 3/4 * x.
According to the riddle, these three numbers add up to 126. So, we can make an equation out of it:
1/2 * x + 3/4 * x + x = 126
Now that we have a simple equation, it's time to put on our mathematical clown shoes!
Combining like terms, we get:
5/4 * x + x = 126
Multiplying both sides by 4 to get rid of the pesky fraction, we have:
5x + 4x = 504
Simplifying this equation further, we get:
9x = 504
Dividing both sides by 9, we find that:
x = 56
So, Curly, the largest number, is 56. Larry, the smallest number, would be half of Curly, which is 1/2 * 56 = 28. Finally, Moe, the middle number, would be 3/4 of Curly, which is 3/4 * 56 = 42.
Therefore, the three numbers from smallest to largest are: 28, 42, and 56. Larry, Moe, and Curly would be very proud! Woob-woob-woob!
Let's represent the smallest number as x, the middle number as y, and the largest number as z.
According to the given information:
1) The smaller number is half the larger number: x = 0.5z
2) The middle number is 3/4 the larger number: y = 0.75z
We are also given that the sum of the three numbers is 126: x + y + z = 126
To solve the problem, we can use the given equations to form a system of equations.
Let's substitute the values of x and y in terms of z into the sum equation:
0.5z + 0.75z + z = 126
Combining like terms:
2.25z = 126
Now, let's solve for z by dividing both sides of the equation by 2.25:
z = 126 / 2.25 = 56
Substituting the value of z back into the equations for x and y:
x = 0.5z = 0.5 * 56 = 28
y = 0.75z = 0.75 * 56 = 42
Therefore, the three numbers, in order from smallest to largest, are: 28, 42, and 56.
To find the three even numbers that sum up to 126, we can set up a system of equations based on the given information. Let's denote the smallest number as "x," the middle number as "y," and the larger number as "z."
According to the problem, the smaller number is half the larger number. This can be represented as:
x = (1/2)z ---- (Equation 1)
The middle number is 3/4 the larger number:
y = (3/4)z ---- (Equation 2)
The sum of the three numbers is 126:
x + y + z = 126 ---- (Equation 3)
Now, we can solve this system of equations to find the values of x, y, and z.
Substituting Equation 1 and Equation 2 into Equation 3, we get:
(1/2)z + (3/4)z + z = 126
Simplifying the expression:
(4/8)z + (6/8)z + (8/8)z = 126
Combining like terms:
(18/8)z = 126
Dividing both sides by (18/8), we have:
z = (126 * 8) / 18
z = 56
Now that we have the value of z, we can substitute it back into Equation 1 and Equation 2 to find the values of x and y.
Substituting z = 56 into Equation 1:
x = (1/2)(56)
x = 28
Substituting z = 56 into Equation 2:
y = (3/4)(56)
y = 42
Therefore, the three numbers, listed in order from smallest to largest, are:
28, 42, 56