How do we set up this problem. The product of a number and 6 is decreased by 8. The result is 13 greater than the product of 4 and the same number increased by 3. What is the number?
He set it up like follows:
6N-8=4N+3
6N-4N=8+3
2N=11
N=11/2
but I can't figure out where the 13 should have been in the problem because the answer in my grader is 33/2. We tried adding it to the 6N -8 side or adding it to the other side but nothing comes up with the answer and we can't figure out what we are doing wrong or my grader is wrong. Please help if you can. Thanks
6n-8 = 13 + 4(n+3)
6n-8 = 13+4n+12
2n = 33
n = 33/2
Thank you ☺
To help you understand the problem and find where the 13 should be, let's break down the problem step by step:
1. "The product of a number and 6 is decreased by 8." We can represent this as 6N - 8, where N is the unknown number.
2. "The result is 13 greater than the product of 4 and the same number increased by 3." We can represent this as 4N + 3 + 13. The 4N represents the product of 4 and the same number, and then we add 3 and 13 to it.
Combining these two representations, we get the equation:
6N - 8 = 4N + 3 + 13
To solve this equation, we can simplify and isolate the variable N, which represents the unknown number:
6N - 8 = 4N + 16
Subtract 4N from both sides of the equation:
6N - 4N - 8 = 4N - 4N + 16
Simplifying further:
2N - 8 = 16
Then, add 8 to both sides of the equation:
2N - 8 + 8 = 16 + 8
Simplifying further:
2N = 24
Finally, divide both sides of the equation by 2 to solve for N:
2N/2 = 24/2
This gives us:
N = 12
Therefore, according to this calculation, the value of the number is 12. However, you mentioned that the answer in your grader is 33/2. Let's see if we can find where the discrepancy arises.
If we go back to the original equation and consider the possibility of the 13 being on the other side, it looks like this:
6N - 8 = 4N + 3 - 13
Simplifying:
6N - 8 = 4N - 10
Then, subtract 4N from both sides:
6N - 4N - 8 = 4N - 4N - 10
Simplifying further:
2N - 8 = -10
Add 8 to both sides:
2N - 8 + 8 = -10 + 8
Simplifying:
2N = -2
Divide both sides by 2:
2N/2 = -2/2
This gives us:
N = -1
Therefore, if we add the 13 to the other side of the equation, we find that the answer is -1, which is different from what your grader suggests.
Based on the information you provided, it appears there may be an error in the calculation or grading. Please review the problem and make sure all the details are accurate. If you have any further questions, feel free to ask.