Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I have been working diligently on learning to solve word problems. I am going to submit the ones I have been doing in the box below. Would you please look at them and tell me if I am doing it the right way before I attempt to re-take that chapter 1 test?
I know it is a lot of extra work for you, but I am not at all sure I am doing this the right way. (If I have submitted too much, just let me know and next time I will only submit one question per form).
I still need to work some more on the Geometry word problems. That will be tomorrow's task!!
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1. A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3000, how much will be invested in each type of investment?
bonds = x + 3,000
CD = 20,000 - x
If I let (x+3,000) represent bonds and (20,000 – x) represent Cd’s I could say.
x + 3,000 = 20,000
x = 20,000 – 3,000
x = 17,000
Divide the 17,000 by 2 gives you $8,500 (which gives you the amount for the Cd)
Then take the 20,000 subtract the 8,500 = $11,500 (the amount for the Bonds)
You got the right result but didn't use the equations quite correctly.
Your first few lines are on the right track, and read as follows:
bonds = x + 3,000
CD = 20,000 - x
If I let (x+3,000) represent bonds and (20,000 – x) represent Cd’s I could say.
x + 3,000 = 20,000
Note that you never stated what x represents, which should be one of the first things you do.
Your equation is fairly close, but it doesn't quite follow from your reasoning.
x + 3000 is the amount in bonds.
So the equation x + 3000 says that the amount in bonds is 20 000. This is clearly not so, since 20 000 represents the amount in both CDs and bonds.
The correct equation represents the fact that
amount in CDs + amount in bonds = 20 000.
According to the above the amount in bonds is x + 3000. Since the amount in bonds exceeds that in CDs by $3000, the amount in CDs must be x. I believe this is what you were assuming, but in your solution you never actually stated what x was. However, the amount in CDs is apparently x, and not 20 000 - x.
Thus
amount in CDs + amount in bonds = 20 000,
amount in CDs = x
amount in bonds = x + 3000.
It follows that
x + x + 3000 = 20 000.
We easily solve for x:
2 x + 3000 = 20 000
2 x = 17 000 so
x = 8500.
x stands for the amount in CDs, which we conclude to be $8500.
x + 3000 = 8500 + 3000 = 11 500, so we conclude that $11 500 is invested in bonds.
2. A total of $10,000 is to be divided between Sean and George, with George to receive $3000 less than Sean. How much will each receive?
10,000 / 2
George = x – 3,000
Sean = 10,000 – x
10,000/2 = 5,000
x – 3,000 = 5,000
x = 5,000 + 3,000
x = 8,000
10,000 – 8,000 = 2,000
George received $2,000 and Sean received $8,00.
You don't say what x represents. Since you say 'george = x - 3000' and george is to receive $3000 less than Sean, you must mean x to represent the amount received by Sean.
Since
george's amt + sean's amt = 10 000, we have
x - 3000 + x = 10 000, which we solve for x to obtain
x = 6500.
This is seans amt.
george's amt is x - 3000 = 6500 - 3000 = 3500.
3. In Nov 2005, Google and Yahoo search engines were used to conduct a total of 3.57 billion on line searches. Google was used to conduct 0.53 billion more searches than Yahoo. How many searches were conducted on each search engine?
3.57 b = total searches
Yahoo = x
Google = x + 0.53
3.57/2 = 1.79
there is nothing in the problem related to half of the total 3.57 billion
this is what you would get if the revenue was equally divided, but that's not the case; calculating this appears to have led you down a wrong path
x + 0.53 = 1.79
the given info is that
yahoo + google = 3.57.
You have already stated that x stands for yahoo's total, and x + 0.53 for google's. So the equation is
x + x + .053 = 3.57, which we can easily solve to get
x = 1.52.
This is interpreted as saying that yahoo's total is $1.52 billion.
Google's total is x + 0.53 = 1.52 + 0.53 = 2.05, meaning that google's total is $2.05 billion.
4. Judy and Tom agree to share the cost of an $18.00 pizza based on how much each ate. If Tom ate 2/3 the amount that Judy ate, how much should each pay? (some pizza may be left)
cost = $18.00 for 100% of pizza
Judy = x
Tom = 2/3(x) of 100%
2/3(x) = 100 divide 100% by 2/3
there is no reason to associate 2/3 x with 100%.
You aren't completely specific about x, but I assume you mean x to represent the amount Judy owes.
Tom ate 2/3 as much so he owes 2/3 x.
The total amount owed is $18.00 so
x + 2/3 x = $18.00.
If you solve this equation for x you get x = $10.80, which is the amount Judy owes.
Then Tom owes 2/3 x = 2/3 ( $10.80) = $7.20.
See my notes above. I'll respond to the other four questions soon after this posting.