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
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?
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.
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?
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.
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
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.