Find 3 consecutive odd numbers such that the sum of 5 times the smaller number a twice the larger number is 33 more than six times the median number.

Do not understand word problems. ..please help

I am going to call the middle number x, then the smaller is x-2, and the larger is x+2

Now just translate the English to Math:
the sum of ----> +
5 times the smaller ---> 5(x-2)
number a twice the larger ---> 2(x+2)

the sum of 5 times the smaller number a twice the larger number ---> 5(x-2)+2(x+2)
is ---> =
33 more than six times the median number --> 6x+33

5(x-2) + 2(x+2) = 6x + 33
5x-10+2x+4=6x+33
x = 39

the numbers are 37, 39, and 41

check:
5(37) + 2(41) = 267
6(39) + 33 = 267
My answer is correct

No problem! Word problems can sometimes be tricky, but I'll help you break it down step by step.

Let's take this problem one piece at a time. The question asks us to find 3 consecutive odd numbers. Let's call the smallest one "x". Since they are consecutive, the next two consecutive odd numbers will be "x + 2" and "x + 4".

Now, let's tackle the second part of the problem. It says that the sum of 5 times the smaller number and twice the larger number is 33 more than six times the median number.

So the sum of 5 times the smaller number (5x) and twice the larger number (2 * (x + 4)) is equal to 33 more than six times the median number (6 * (x + 2) + 33).

Now we can set up an equation:

5x + 2 * (x + 4) = 6 * (x + 2) + 33

Next, we simplify the equation:

5x + 2x + 8 = 6x + 12 + 33

Combine like terms:

7x + 8 = 6x + 45

Subtract 6x from both sides:

7x - 6x + 8 = 45

Simplify further:

x + 8 = 45

Now, subtract 8 from both sides:

x = 45 - 8

x = 37

So the smallest odd number is 37.

The next odd number is x + 2:

37 + 2 = 39

The third odd number is x + 4:

37 + 4 = 41

Therefore, the three consecutive odd numbers are 37, 39, and 41.

Sure! Let's break down the problem step by step.

Step 1: Let's represent the first odd number as "x". Since we're looking for consecutive odd numbers, the second odd number would be "x + 2" and the third odd number would be "x + 4".

Step 2: We need to translate the given information into an equation. The sum of 5 times the smaller number and twice the larger number is written as: 5x + 2(x + 4).

Step 3: The phrase "is 33 more than six times the median number" can be translated into the following equation: 5x + 2(x + 4) = 6(x + 2) + 33.

Step 4: Simplify both sides of the equation. On the left side, distribute the values and combine like terms. On the right side, distribute and combine like terms as well.

5x + 2x + 8 = 6x + 12 + 33

Step 5: Simplify further.

7x + 8 = 6x + 45

Step 6: Move all terms involving "x" to one side of the equation and all constants to the other side.

7x - 6x = 45 - 8

x = 37

Step 7: Now that we have the value of "x", we can find the three consecutive odd numbers.

The first odd number is x = 37.
The second odd number is x + 2 = 37 + 2 = 39.
The third odd number is x + 4 = 37 + 4 = 41.

So, the three consecutive odd numbers are 37, 39, and 41.