At the start of the week, the amount of money in Howard's bank account varies directly with the number of hours he worked and inversely with the number of hours he spent shopping the past week. If has $2,000 in his bank account the week after spending 25 hours working and 4 hours shopping, how much does he have the week after spending 40 hours working and 1 hours shopping?
m = kh/s
2000 = k*25/4
k = 320, so
m = 320h/s
Now just plug in your work/shop hours to find m.
To find out how much Howard has in his bank account the week after spending 40 hours working and 1 hour shopping, we can use the concept of direct and inverse variation.
Let's start by identifying the variables in this problem:
- x: the number of hours Howard worked
- y: the number of hours Howard spent shopping
- M: the amount of money in Howard's bank account
Given that the amount of money in Howard's bank account varies directly with the number of hours he worked and inversely with the number of hours he spent shopping, we can set up the following equation:
M = k * (x/y)
where k is the constant of variation.
Now, let's use the information given in the problem to find the value of k. We know that when Howard spent 25 hours working and 4 hours shopping, he had $2,000 in his bank account. Substituting these values into the equation, we get:
2000 = k * (25/4)
To find k, we can solve this equation for k:
k = 2000 * (4/25)
k = 320
Now that we have the value of k, we can use it to find out how much Howard has in his bank account the week after spending 40 hours working and 1 hour shopping. We substitute x = 40 and y = 1 into the equation:
M = 320 * (40/1)
M = 320 * 40
M = 12,800
Therefore, Howard has $12,800 in his bank account the week after spending 40 hours working and 1 hour shopping.