Tutors Answer Your Questions about Equations (FREE)
Question 286926: We're doing review now and i do not remember how to do words problems like this. Here is the problem: Two boats traveled in opposite directions from the same starting point. The rate of one boat was 10km per hour faster than the rate of the other. After 3 hours they were 270km apart. Find the rate of the slower boat.
Click here to see answer by richwmiller(17219)   |
Question 286926: We're doing review now and i do not remember how to do words problems like this. Here is the problem: Two boats traveled in opposite directions from the same starting point. The rate of one boat was 10km per hour faster than the rate of the other. After 3 hours they were 270km apart. Find the rate of the slower boat.
Click here to see answer by josmiceli(19441)  |
Question 287174: old rectangle with dimensions of 12x8
new rectangle has length of 15
what is the new width of the rectangle so it's dimensions are proportional to the old rectangle?
Okay, so I know the correct answer and how you get it but I still have a question.
Answer: 12/8=15/x, x being the width. x=10 is the correct answer but i'd like to know if there is a way of getting that answer by using the area instead. this is what i did:
12 old length/96 old area =15 new length/(A)new area
A=120
8 old width/96 old area=(w)new width/120 new area
W=10
10 is the correct answer but i wanted to know if i did it correctly, or if it is wrong and i just happen to get the same answer.
thanks!!!
Click here to see answer by richwmiller(17219) |
Question 287606: How do you know what the graph of 5x - 9y^2 = 12 - 4y is? I tried to compare it to the graphs of a circle, ellipse and hyperbola, however, the only plausible answer is a parabola...is this correct? I know the formula for a parabola is y=ax^2+bx+c, however the coefficients are turned around in the equation. Thank you.
Click here to see answer by scott8148(6628)  |
Question 288037: [Problem]
On a string of 15 pearls, the centre pearl is the largest and most expensive. Starting from one end and including the centre pearl, each pearl is worth R50 more than the previous one. Starting from the other end and including the centre pearl, each pearl is R25 more than the previous one. The total value of the pearls is R 4 650. What is the value of the centre pearl?
[Thoughts]
Okay, I can see that, this is an arithmetic series problem.
I can see that the middle term is the centre pearl, the 8th pearl in the middle of the string of 15 pearls (n=8) and it is the most expensive, meaning that counting from one end (say, from left to right) with a common difference of d=50 (R50) , and including the centre pearl will only account for the first 8terms. Because, the middle term (8th term) is greater in price, hence the 9th term cannot be R50 more that the previous one (which is the 8th term)
The same occurs with the R25 difference, counting from one end (say, from right to left) with a common difference of d=25 (R25) ,and including the centre pearl will only account for the first 8terms. Because, the middle term (8th term) is greater in price, hence the 9th term (pearl) cannot be R25 more that the previous one (which is the 8th term).
Now , this leaves me with 2 sets of arithmetic calculations. First one : d=50, n=8 An=? (An is the centre pearl, counting from left to right) .
Using the equation: An = a1 + (n-1) d (a1 =denotes first term on the right end)
= a1 + 7 (50)
= a1 + 350
The second one is: d=25, n=8 An=? (Again , An is the centre pearl, from right to left) .
Using the equation: An = a + (n-1) d (a =denotes first term on the right end)
= a + 7 (25)
= a + 175
From the above 2 equations, I get that: An=a1 + 350= a + 175
a1 + 350= a + 175
a = a1 + 175. . . . . . . . . .(1)
The total value of the 15 pearls = 4650 , hence meaning that Sn = 4650 and therefore
Sn = n/2 [a1+An] + n/2 [a + An]
4650 = 8/2 [a1 + (a1 + 350)] + 8/2 [ a + (a + 175) ]
4650 = 8a1 + 1400 + 8a + 700
4650 = 8a1 + 8a + 2100
2550 = 8a1 + 8a
then, substituting eqtn (1), I get . . .
2550 = 8a1 + 8 (a1 + 175)
1150 = 16a1
a1 = 72
then, substituting in the eqtn : An = a1 + 350
= (72) + 350
= 422
Therefore, I get centre pearl to be R 422 .
[Difficulty]
My problem is , summing up ALL the terms does not give me R 4650 . Where did I go wrong?
Click here to see answer by toidayma(44)  |
Question 288184: The price of a magazine subscription rose 4% this year. If the subscription now costs $26, how much did it cost last year?
I used $26 divided by .04 = $850. I took $26.00 and subtracted $$8.50 to equal $19.50 which looks about right to me, but the decimal was in the wrong place, so I don't know what formula I should have used, because this one is definitely wrong.
Please tell me the correct formula to use! (The problem below is not a second problem, just another problem with a known answer that I used to attempt to figure out the formula for the actual question above)
I've been using the problem: "The price of a computer fell 20% this year. If the computer now costs $750, how much did it cost last year?" to figure out how to solve the above problem since I know the correct answer to the computer problem is $ 937.50, but I can't solve it.
I used:
$750 divided by 20= $150, then added $750 to $150 to equal $900, which is $37.50 short of the book's answer of $937.50. Each way I've tried brings me to $900.
Click here to see answer by richwmiller(17219) |
Question 288228: What formula would I use to solve this problem?
A radiator contains 6 liters of a 25% anti-freeze solution. How much should be drained and replaced with pure anti-freeze to produce a 33% solution?
I've been working on a similar problem that I know the answer to in order to figure out how to solve this problem, but I can't seem to find the correct formula for either one.
My most recent attempt was:
6(.25 -x) + 1x = 6(.33)
6.25-6x+x=1.98
4.23-5x=0
4.23=5x
x=.846
This didn't work for the other problem, so I know this can't be correct here, either.
Could someone explain the correct formula to me?
My book doesn't cover percent mixture problems very in depth, just touches on one type and then moves on. Thanks for any help given!
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 288255: Okay, here goes another easy one that I can't solve:
Printer A can print a report in 3 hours.
Printer B can print a report in 4 hours.
How long would it take for both printers, working together, to print the report?
I've used several different formulas and can answer the practice questions correctly, but I'm not sure HOW I'm answering them correctly, because I don't understand why I'm using this formula.
Last attempt I used:
t over 4 plus t over 3 = 1 report
t over 4 multiplied by 3 = 3t over 12
t over 3 multiplied by 4 = 4t over 12
3t plus 4t over 12 = 7t over 12
so, 7t over 12 = 1 report.
I multiply each side by 12 (this is where I start to wonder what I'm doing...)
So I have 84t over 12 = 12 or I have 7t = 12,
which results in:
t = 1 and 5 over 7.
Can this possibly be right?
If so, why did I multiply each side by 12 or was I supposed to divide before dividing again?
I understand the problem in the book, but it uses 3 and 6 and I've tried several different ways,
but they all come up with the correct answer of "2", so I don't know which formula is correct or why I keep getting the right answer even though I don't know what I'm doing.
Any help or explanation is greatly appreciated, thank you!
Click here to see answer by amnd(23)  |
Question 1758: I'm taking an algebra class for the first time in years and cannot remember how to solve this:i had got this answer x=6.
The answer should be 6 but i can't figure out how to solve. Thanks for any help.
Click here to see answer by Atato(1) |
Question 288620: I don't know how to write an equation for this. Please help due today!
How many different license plates are possible if each contains three letters followed by three digits? The letters may repeat although the letters I and O are not used and the digits may repeat?
Click here to see answer by richwmiller(17219) |
Question 288620: I don't know how to write an equation for this. Please help due today!
How many different license plates are possible if each contains three letters followed by three digits? The letters may repeat although the letters I and O are not used and the digits may repeat?
Click here to see answer by dabanfield(803) |
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