Need help with these 3, with work shown please---
30. A block of ice loses one-third of its weight every hour. After 2 hours, the block weighs 40 pounds. How much did the block of ice weigh to begin with?
48. Does the Commutative Property apply to this situation? I ate dinner and read a book.
50. You work for FunMath, Inc. It is your job to describe the financial future of your beloved company. You just started, and the last person didn't do a good job of record keeping. In fact, the last person only has two years data. After going through all the old files, you only found the following information: in 1989 FunMath Inc. made a profit of $3,720.00 and in 1994 FunMath, Inc. made a profit of $7,480. Your boss would like to know what 2003's profit will be based on this limited information. Assume that FunMath's profits act linearly.
a. $11,240.00
b. $752.00
c. $14,248.00
I think this might be A
Thanks
-MC
Ok. Here is what I am thinking. As the student, you will need to see if I am also thinking this correctly.
30. If the the block weighs 40 pounds now (after 2 hours), and the block losses 1/3 of its weight every hour, then it has lost 2/3 (2 hours of losing 1/3 is 2/3) so far. It has 1/3 left (40 pounds). If 40 is 1/3 of its weight, then you can figure out how much it started with. 1/3 + 1/3 + 1/3 = the starting weight. 40 + 40 + 40 = ? (I've done more than enough). You can finish thes up for me.
48. Commutative property means that you can do it more than one way. The sentence stated that you ate AND had dinner. It didn't state in which order you did it in. So is it commutative?
50. To figure this one out, I noticed that you were given two year's profits (1989 and 1994). By subtracting the two profits, I saw that there was a $3760 increase in 1994 than 1989. I originally agreed with you on your answer, but as I was typing this I asked myself what year is it wanting? 2003 is not 5 years difference. It is 9. You may need to add $3760 twice. I have not done that, so please see if I'm right. I do not think A is the correct answer.
just my thought on #30
Since it loses 1/3 of its weight each hour and after 2 hours it weighs 40 lbs,
then one hour ago it must have weighed 40 ÷ (2/3) lbs or 60 lbs. (check take 1/3 of 60 and subtract)
then 2 hours ago it must have weighed 60 ÷ (2/3) or 90 lbs.
check: take 1/3 of 90 away ---> 60
take 1/3 of 60 away --> 40, my answer is correct.
I believe Reiny may be right. I sometimes miss the "tricky" aspect of the questions.
30. 90 lbs
48. yes
50. c, $14,248.00
30. To solve this problem, you can set up an equation using the information given. Let's say the weight of the block of ice to begin with is represented by the variable 'x'. We can then set up the equation:
x - (1/3)x = 40
Here, "(1/3)x" represents one-third of the weight of the block lost every hour. Simplifying the equation, we have:
(2/3)x = 40
To isolate 'x', we can multiply both sides of the equation by the reciprocal of (2/3), which is (3/2):
(3/2)(2/3)x = (3/2)(40)
x = 60
Therefore, the block of ice originally weighed 60 pounds.
48. The Commutative Property states that the order of the numbers being added or multiplied does not affect the result. In this situation, the Commutative Property does not apply because the order of the actions 'ate dinner' and 'read a book' does affect the overall outcome. It makes a difference whether you ate dinner and then read a book, or if you read a book and then ate dinner.
50. To determine the future profit for 2003 based on the limited information, we can use the concept of linear regression. Linear regression helps us find the equation of a straight line that best fits the given data points. We can use the information about profits in 1989 and 1994 to estimate the profit in 2003.
First, let's find the slope of the line, which represents the rate of change in profit per year:
Slope = (profit in 1994 - profit in 1989) / (year for 1994 - year for 1989)
Slope = ($7,480 - $3,720) / (1994 - 1989)
Slope = $3,760 / 5
Slope = $752
Now that we have the slope, we can find the equation of the line using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is any point on the line.
Choosing the point (1989, $3,720) as our reference:
y - $3,720 = $752(x - 1989)
To find the profit in 2003, we substitute x = 2003 into the equation:
y - $3,720 = $752(2003 - 1989)
y - $3,720 = $752(14)
y - $3,720 = $10,528
y = $10,528 + $3,720
y = $14,248
Therefore, the estimated profit for FunMath, Inc. in 2003 based on the limited information is $14,248.
So, option C, $14,248.00, is the correct answer.