Question
It takes a woman 12 minutes to drive one way to work. She goes home for lunch 3 days each week. How much time does she spend driving to and from work each 5-day work week?
2 hours, 36 minutes
3 hours
3 hours, 12 minutes
3 hours, 20 minutes
none of these
2 hours, 36 minutes
3 hours
3 hours, 12 minutes
3 hours, 20 minutes
none of these
Answers
GPT 3.5
3 hours, 12 minutes
Explanation:
Each day she spends 12 minutes driving to work and 12 minutes driving home, so in total it takes her 24 minutes each day.
Therefore, in a 5-day work week, she spends a total of 24 minutes x 5 days = 120 minutes driving to and from work.
This is equivalent to 2 hours, 120 minutes รท 60 minutes = 2 hours, 0 minutes.
So the total time she spends driving to and from work each 5-day work week is 2 hours + 2 hours = 4 hours.
Adding the time she spends going home for lunch 3 days each week (3 days x 24 minutes = 72 minutes), the total time is 4 hours + 1 hour 12 minutes = 5 hours, 12 minutes.
Therefore, the closest answer is 3 hours, 12 minutes.
Explanation:
Each day she spends 12 minutes driving to work and 12 minutes driving home, so in total it takes her 24 minutes each day.
Therefore, in a 5-day work week, she spends a total of 24 minutes x 5 days = 120 minutes driving to and from work.
This is equivalent to 2 hours, 120 minutes รท 60 minutes = 2 hours, 0 minutes.
So the total time she spends driving to and from work each 5-day work week is 2 hours + 2 hours = 4 hours.
Adding the time she spends going home for lunch 3 days each week (3 days x 24 minutes = 72 minutes), the total time is 4 hours + 1 hour 12 minutes = 5 hours, 12 minutes.
Therefore, the closest answer is 3 hours, 12 minutes.
A business buys invoice forms at a cost of $4.45 a box for the first 20 boxes, $4.00 a box for the next 25 boxes, and $3.75 a box for any additional boxes. How many boxes of invoice forms can be bought for $234.00?
GPT 3.5
Let's denote:
- x as the number of boxes of invoice forms that were bought for $4.45 a box
- y as the number of boxes of invoice forms that were bought for $4.00 a box
- z as the number of boxes of invoice forms that were bought for $3.75 a box
And since the total cost of the boxes of invoice forms is $234:
4.45x + 4.00y + 3.75z = 234
We are also given the information that the business bought 20 boxes at $4.45 each, then 25 boxes at $4.00 each, and any additional boxes at $3.75. So, we know that:
x + y + z = 20
y + z = 25
Solving the above equations simultaneously:
y = 25 - z
x = (20 - (25 - z)) = 20 - 25 + z = z - 5
Now substitute the values back into the first equation:
4.45(z - 5) + 4.00(25 - z) + 3.75z = 234
4.45z - 22.25 + 100 - 4z + 3.75z = 234
-0.20z + 78.75 = 234
-0.20z = 155.25
z = 155.25 / -0.20
z = 776.25
So, the business can buy 776.25 boxes of invoice forms for $234.00. However, since you can't buy a fraction of a box, the maximum number of boxes that can be bought for $234.00 is 776 boxes.
- x as the number of boxes of invoice forms that were bought for $4.45 a box
- y as the number of boxes of invoice forms that were bought for $4.00 a box
- z as the number of boxes of invoice forms that were bought for $3.75 a box
And since the total cost of the boxes of invoice forms is $234:
4.45x + 4.00y + 3.75z = 234
We are also given the information that the business bought 20 boxes at $4.45 each, then 25 boxes at $4.00 each, and any additional boxes at $3.75. So, we know that:
x + y + z = 20
y + z = 25
Solving the above equations simultaneously:
y = 25 - z
x = (20 - (25 - z)) = 20 - 25 + z = z - 5
Now substitute the values back into the first equation:
4.45(z - 5) + 4.00(25 - z) + 3.75z = 234
4.45z - 22.25 + 100 - 4z + 3.75z = 234
-0.20z + 78.75 = 234
-0.20z = 155.25
z = 155.25 / -0.20
z = 776.25
So, the business can buy 776.25 boxes of invoice forms for $234.00. However, since you can't buy a fraction of a box, the maximum number of boxes that can be bought for $234.00 is 776 boxes.
A student returned 4 overdue books to the library. The fine for each overdue book is $0.35 for the first day, $0.40 for each of the next 3 days, and $0.45 for each day after that. The total fine was $13.40. How many days overdue were the books?
GPT 3.5
Let's denote:
- x as the number of days the books were overdue at $0.35 per day
- y as the number of days the books were overdue at $0.40 per day
- z as the number of days the books were overdue at $0.45 per day
We know that:
x + y + z = total number of days the books were overdue
The total fine was $13.40, so we can set up the equation:
0.35x + 0.40y + 0.45z = 13.40
Given that 4 books were returned, we have:
x + y + z = 4
We now have a system of equations to solve:
x + y + z = 4
0.35x + 0.40y + 0.45z = 13.40
From the first equation, we can express x in terms of y and z:
x = 4 - y - z
Substitute x into the second equation:
0.35(4 - y - z) + 0.40y + 0.45z = 13.40
1.4 - 0.35y - 0.35z + 0.40y + 0.45z = 13.4
-0.05y + 0.1z = 12
Now we have two equations:
y + z = 4
-0.05y + 0.10z = 12
By testing values, we find that y = 8 and z = 4. So the books were overdue by:
x = 4 - 8 - 4 = -8
Since it doesn't make sense for the books to be overdue for a negative number of days, there must be an error in the initial calculations. Let's reassess the equations and solve the problem.
- x as the number of days the books were overdue at $0.35 per day
- y as the number of days the books were overdue at $0.40 per day
- z as the number of days the books were overdue at $0.45 per day
We know that:
x + y + z = total number of days the books were overdue
The total fine was $13.40, so we can set up the equation:
0.35x + 0.40y + 0.45z = 13.40
Given that 4 books were returned, we have:
x + y + z = 4
We now have a system of equations to solve:
x + y + z = 4
0.35x + 0.40y + 0.45z = 13.40
From the first equation, we can express x in terms of y and z:
x = 4 - y - z
Substitute x into the second equation:
0.35(4 - y - z) + 0.40y + 0.45z = 13.40
1.4 - 0.35y - 0.35z + 0.40y + 0.45z = 13.4
-0.05y + 0.1z = 12
Now we have two equations:
y + z = 4
-0.05y + 0.10z = 12
By testing values, we find that y = 8 and z = 4. So the books were overdue by:
x = 4 - 8 - 4 = -8
Since it doesn't make sense for the books to be overdue for a negative number of days, there must be an error in the initial calculations. Let's reassess the equations and solve the problem.
A student returned 4 overdue books to the library. The fine for each overdue book is $0.35 for the first day, $0.40 for each of the next 3 days, and $0.45 for each day after that. The total fine was $13.40. How many days overdue were the books?
6
8
18
20
none of these
6
8
18
20
none of these
GPT 3.5
Let's denote:
- x as the number of days the books were overdue at $0.35 per day
- y as the number of days the books were overdue at $0.40 per day
- z as the number of days the books were overdue at $0.45 per day
From the information provided, we know that:
x + y + z = total number of days the books were overdue (1)
0.35x + 0.40y + 0.45z = 13.40 (2)
Given that 4 books were returned, we also know that:
x + y + z = 4 (3)
From (1) and (3), we have:
4 = 4
Therefore, the first and third equations are consistent.
Substitute the value of x from equation (3) into equation (2):
0.35(4-y-z) + 0.40y + 0.45z = 13.40
1.4 - 0.35y - 0.35z + 0.40y + 0.45z = 13.40
0.05y + 0.1z = 12
Dividing throughout by 0.05, we get:
y + 2z = 240
Now, we need to find values of y and z that satisfy the above equation. Since there is no integer solution for y and z that satisfies the equation, we need to reevaluate the problem. Let's reconsider the information and our calculations.
- x as the number of days the books were overdue at $0.35 per day
- y as the number of days the books were overdue at $0.40 per day
- z as the number of days the books were overdue at $0.45 per day
From the information provided, we know that:
x + y + z = total number of days the books were overdue (1)
0.35x + 0.40y + 0.45z = 13.40 (2)
Given that 4 books were returned, we also know that:
x + y + z = 4 (3)
From (1) and (3), we have:
4 = 4
Therefore, the first and third equations are consistent.
Substitute the value of x from equation (3) into equation (2):
0.35(4-y-z) + 0.40y + 0.45z = 13.40
1.4 - 0.35y - 0.35z + 0.40y + 0.45z = 13.40
0.05y + 0.1z = 12
Dividing throughout by 0.05, we get:
y + 2z = 240
Now, we need to find values of y and z that satisfy the above equation. Since there is no integer solution for y and z that satisfies the equation, we need to reevaluate the problem. Let's reconsider the information and our calculations.
Related Questions
Enter your answer and show all the steps that you use to solve this problem in the space provided....
Note: Enter your answer and show all the steps that you use to solve this problem in the space provi...
It takes a woman 12 minutes to drive one way to work. She goes home for lunch 3 days each week. How...