Find four consecutive even integers such that four times the greatest is 36 more than more than the sum of the other three.Four times a number increased by 5 is 37.Find the number.
If " n " is an integer, then n, n + 2, n + 4 and n + 6 will be even consecutive integers.
Four times the greatest is 36 more than more than the sum of the other three.
This mean :
4 ( n + 6 ) = 36 + ( n + n + 2 + n + 4 )
4 ( n + 6 ) = 36 + ( n + n + 2 + n + 4 )
4 * n + 4 * 6 = 36 + 3 n + 2 + 4
4 n + 24 = 42 + 3 n Subtract 3 n to both sides
4 n + 24 - 3 n = 42 + 3 n - 3 n
n + 24 = 42 Subtract 24 to both sides
n + 24 - 24 = 42 - 24
n = 18
So consecutive even integers are :
18
18 + 2 = 20
18 + 4 = 22
18 + 6 = 24
Proof :
4 * 24 = 36 + 18 + 20 + 22
96 = 96
Why did the even integers go to the comedy club? Because they wanted to have a sum-thing to laugh about!
Let's solve the problem step by step:
1. Let's represent the four consecutive even integers as n, n+2, n+4, and n+6.
2. According to the problem, four times the greatest is 36 more than the sum of the other three. So we have the equation: 4(n+6) = (n + n+2 + n+4) + 36.
3. Simplifying the equation, we get: 4n + 24 = 3n + 6 + 36.
4. Combining like terms, we have: 4n = 3n + 42.
5. Subtracting 3n from both sides, we get: n = 42.
Therefore, the four consecutive even integers are 42, 44, 46, and 48.
Now let's tackle the second problem:
1. Let's represent the number as n.
2. According to the problem, four times the number increased by 5 is 37. So we have the equation: 4n + 5 = 37.
3. Subtracting 5 from both sides, we get: 4n = 32.
4. Dividing both sides by 4, we get: n = 8.
Therefore, the number is 8.
Remember, math problems may seem tough, but with a little humor and perseverance, you can solve them!
Let's solve each problem step-by-step:
1) Find four consecutive even integers such that four times the greatest is 36 more than the sum of the other three:
Let's assume the first even integer is "x". Since they are consecutive even integers, the second would be "x + 2", the third would be "x + 4", and the fourth would be "x + 6".
Now, we can set up the equation based on the given information:
4(x + 6) = (x + x + 2 + x + 4) + 36
Simplifying the equation:
4x + 24 = 3x + 6 + 36
4x - 3x = 42 - 24
x = 18
Therefore, the four consecutive even integers are 18, 20, 22, and 24.
2) Four times a number increased by 5 is 37:
Let's assume the number is "x".
Now, we can set up the equation based on the given information:
4x + 5 = 37
Solving for "x":
4x = 37 - 5
4x = 32
x = 32/4
x = 8
Therefore, the number is 8.
To solve this problem, we need to set up equations based on the given information and then solve the equations to find the solution.
Let's start with the first problem: finding four consecutive even integers.
Let's assume the four consecutive even integers are x, x+2, x+4, and x+6.
According to the problem, four times the greatest integer is 36 more than the sum of the other three. We can translate this information into an equation:
4(x+6) = (x + x+2 + x+4) + 36
Now we can solve this equation to find the value of x:
4x + 24 = 3x + 6 + 36
4x - 3x = 36 - 6 - 24
x = 6
So the four consecutive even integers are 6, 8, 10, and 12.
Now let's move on to the second problem: finding the number when four times a number increased by 5 is 37.
Let's assume the number is x.
According to the problem, 4x + 5 = 37. We can solve this equation to find the value of x:
4x = 37 - 5
4x = 32
x = 32/4
x = 8
So the number is 8.
In both problems, we set up equations based on the given information and then solved the equations to find the solutions.