An office manager reported that he spent $350 on gifts for employees. He said that $240 was spent on clothing with each man receiving a $20 T-shirt and each woman receiving a $40 sweatshirt. He said that $110 was spent on desk accessories with each man receiving a $5 calendar and each woman receiving a $15 stapler. If m equals the number of men and wequals the number of women, the system of equations that represents the expenses is as follows:

Question

An office manager reported that he spent $350 on gifts for employees. He said that $240 was spent on clothing with each man receiving a $20 T-shirt and each woman receiving a $40 sweatshirt. He said that $110 was spent on desk accessories with each man receiving a $5 calendar and each woman receiving a $15 stapler. If m equals the number of men and wequals the number of women, the system of equations that represents the expenses is as follows:

m+2w=12
m+3w=22

Solve the system, showing all steps, and then discuss the reasonableness of the answer.

I don't know what I am supposed to do on this question, i'm not sure if they are talking about the m+2w=12 system or the If m equals the number of men and w equals the number of women, the system of equations that represents the expenses is as follows. Its just very confusing to me (probably because I am stupid)

Answer 1

(I am Reiny , but not using my regular IP address)

This is a poorly worded question, so you are not stupid.
1st equation: 20m + 40w = 240
divided each term by 20
m + 2w = 12
2nd equation : 5m + 15w = 110
divide each term by 5
m + 3w = 22

now subtract them,
w = 10
back into m + 2w = 12
10 + 2w = 12
2w =
w = 1

there were 10 men and 1 woman

Answer 2

thx Reiny2

Answer 3

Thx Reiny2 !!

Answer 4

Don't worry, you're not stupid! Let's break it down step by step.

First, let's establish the two systems of equations given:

1. m + 2w = 12
2. m + 3w = 22

To solve this system, we can use the method of substitution or elimination. Let's use substitution.

From equation 1, we have m = 12 - 2w. Now we substitute this value of m into equation 2:

(12 - 2w) + 3w = 22

Simplifying, we get:

12 + w = 22

Subtracting 12 from both sides:

w = 10

Now that we have the value of w, we can substitute it back into equation 1 to find m:

m + 2(10) = 12
m + 20 = 12
m = 12 - 20
m = -8

So the solution to the system of equations is m = -8 and w = 10.

Now, let's discuss the reasonableness of this answer. From the context given, we know that m represents the number of men and w represents the number of women. Since we can't have a negative number of men, the value of m = -8 is not reasonable in this context.

Therefore, the system of equations does not seem to accurately represent the situation. There might be an error in the problem statement or the given equations. It's best to clarify and double-check the problem to ensure the accuracy of the solution.