New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'oberobic'
oberobic answered: 2303 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309, >>NextGeometry_Word_Problems/669225: Which one of the following is a better buy: a large pizza with a 14-inch diameter for $12.00 or a medium pizza with a 7-inch diameter for $5.00?
1 solutions
Answer 416225 by oberobic(2304)   on 2012-10-20 12:31:15 (Show Source):
You can put this solution on YOUR website!Area = pi * r^2
.
A pizza with a 7-inch diameter has a radius of 3.5 inches.
Area = pi*3.5^2 = 38.48 sq. in.
.
A pizza with a 14-inch diameter has a radius of 7 inches.
Area = pi*7^2 = 153.93 sq. in.
.
The smaller pizza costs $5 = 500 cents, so it costs 500/38.48 = about 13 cents per sq. in.
.
It costs $12 = 1200 cents, so it costs 12/153.93 = about 8 cents per sq in.
.
The larger pizza is a better buy in terms of the cost per sq. in.
.
Done.
|
Rectangles/558711: The perimeter of a rectangle is 208 inches. The length exceeds the width by 52 inches. Find the length and the width.
1 solutions
Answer 363142 by oberobic(2304) on 2012-01-17 20:45:19 (Show Source):
You can put this solution on YOUR website!P = 2*(L+W) = 208
.
L+W = 208/2 = 104
.
L = 104-W
.
L = W+52
.
L=L, so
104-W = W+52
52 = 2W
W = 26
.
L = W+52 = 26+52 = 78
.
Check answer with perimeter.
L+W = 26+78 = 104
P = 2*(L+W) = 2*104 = 208
Correct.
.
Answer: L=78, W=26
.
Done.
|
Travel_Word_Problems/557452: Clark has a boat that can travel at 15kph in still water. It can go 140km with the current at the same time it takes to travel 35km against the current.
what is the speed of the river??
1 solutions
Answer 362614 by oberobic(2304) on 2012-01-15 11:11:18 (Show Source):
You can put this solution on YOUR website!Always start with the basic distance equation: d = r*t, where d=distance, r=rate (or speed), and t=time.
s = speed in still water = 15 km/hr
.
The current in the river may be defined as 'c'.
Going against the current, r = s-c, which means the current slows the boat down.
Going with the current, r = s+c, which means the current speeds the boat along.
.
Going upstream (that is, against the current), the boat goes 15 km.
Going downstream (that is, with the current), the boat goes 140 km.
.
These distances are covered in the same time.
.
d = r*t
so
t= d/r
.
140 = (s+c) * t = (15+c)*t
35 = (s-c) * t = (15-c)*t
.
140/(15+c) = t
35/(15-c) = t
t = t
.
140/(15+c) = 35/(15-c)
.
cross multiply
.
140*(15-c) = 35*(15+c)
2100 - 140c = 525 + 35c
1575 = 175c
c = 1575/175
c = 9
.
check this answer
t = 140/(15+9) = 140/24 = 35/6
t = 35/(15-9) = 35/6
t = t
correct
.
Answer: The river's current is 9 km/hr.
.
Done.
|
Problems-with-consecutive-odd-even-integers/552415: if x represents the smallest of three consecutive integers, what would the largest be represented by?
1 solutions
Answer 360258 by oberobic(2304) on 2012-01-03 22:03:50 (Show Source):
You can put this solution on YOUR website!Three consecutive integers can be defined as:
x
x+1
x+2
.
If you're setting up an equation, you might find defining them as:
x-1
x
x+1
useful, too.
.
Note that consecutive even integers can be defined as:
x
x+2
x+4
.
Interestingly, consecutive odd integers can be defined exactly the same:
x
x+2
x+4
.
Of course, if you had to find numbers that are consecutive multiples of 7, then you could define:
x
x+7
x+14
.
And so forth.
|
Graphs/552413: I am trying to help my daughter with her homework from 1300 miles away please help! The problem is find the equation of a line in slope intercept form with an undefined slope and passes though (3,-2). Thank you so much, it's been a long time since I've done this stuff.
1 solutions
Answer 360251 by oberobic(2304) on 2012-01-03 21:52:46 (Show Source):
You can put this solution on YOUR website!An equation in slope-intercept form is: y = mx + b.
m = slope = the 'rise' over the 'run' or the change in y divided by the change in x.
(0,b) = y-intercept
.
The statement "with an undefined slope" has a distinct mathematical meaning: it means you have a situation where you need to divide by 0.
.
In contrast, 0 can be divided by any number, which yields 0 as the answer.
.
The slope = change in y divided by the change in x.
.
slope = m = (y-y 1) / (x-x 1)
.
To divide by 0 would mean x = x 1.
.
That can only be a vertical line.
.
The vertical line that goes through (3,-2) is simply: x = 3.
This line goes through all of the points from (3, -infinity) to (3, +infinity), where y takes on any value from -infinity to +infinity.
.
Interestingly, the horizontal line that goes through (3,-2) is simply: y = -2. It has a slope = 0.
.
Vertical and horizontal lines are special cases.
|
Number-Line/552408: how to you get what number is between 3/4 and 2/3?
1 solutions
Answer 360247 by oberobic(2304) on 2012-01-03 21:40:10 (Show Source):
You can put this solution on YOUR website!If you wanted to find the number that is half the distance between 3/4 and 2/3, you could multiply the difference by 1/2 and add to the smaller fraction.
.
3/4 = 9/12
2/3 = 8/12
----------------subtract
3/4 -2/3 = 1/12
.
1/2 * 1/12 = 1/24
.
2/3 + 1/24 = 16/24 + 1/24 = 17/24
.
Done.
|
Geometry_Word_Problems/551594: A rectangle has a perimeter of 34 cm and an area of 52 cm. Its length is 5 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.
1 solutions
Answer 359793 by oberobic(2304) on 2012-01-01 22:11:41 (Show Source):
You can put this solution on YOUR website!2(L+W) = 34
L + W = 17
.
L*W = 52
.
L = 2W+5
.
2L + 2W = 34
L - 2W = 5
--------------- add
3L = 39
L = 13
.
L+W = 17
W = 4
.
Check perimeter.
2*(13+4) = 34
Check area.
13*4 = 42
Check relationship between L and W.
L = 2*W + 5 ??
Yes.
.
Answer: Length = 13; Width 4
.
Done.
|
Numbers_Word_Problems/551451: Twice of larger number equals three times the smaller number and their sum is 40.find the numbers.
1 solutions
Answer 359728 by oberobic(2304) on 2012-01-01 15:17:53 (Show Source):
You can put this solution on YOUR website!x + y = 40
x = 40-y
.
2x = 3y
x = 3y/2 = 3/2*y
.
x = x
so
40-y = 3y/2
.
cross multiply
.
2(40-y) = 3y
80 -2y = 3y
80 = 5y
y = 16
.
x = 40-y
x = 40-16
x = 24
.
Does 2x=3y?
2*24=48
3*16=48
Correct.
.
Answer: x=24, y=16
.
Done.
|
Word_Problems_With_Coins/551448: Dj has $4.50 in dimes and quarters. he has 4 more quarters than dimes. How many coins of each type does he have
1 solutions
Answer 359724 by oberobic(2304) on 2012-01-01 14:38:24 (Show Source):
You can put this solution on YOUR website!d = number of dimes
10d = value of the dimes in cents
q = number of quarters
25q = value of quarters in cents
.
10d +25q = $4.50= 450 cents
.
q = d+4
.
10d + 25(d+4) = 450
10d +25d + 100 = 450
35d = 350
d = 10
.
q = 10+4 = 14
.
Check the values.
10*10 = 100
25*14 = 350
100 +350 = 450
Correct.
.
Answer: 10 dimes and 14 quarters
.
Done.
|
Probability-and-statistics/551446: If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?
1 solutions
Answer 359723 by oberobic(2304) on 2012-01-01 14:28:56 (Show Source):
You can put this solution on YOUR website!Given a red card is drown from the deck, then there are 26 total possibilities.
There are 13 ways the cared could be a diamond, which defines the favorable outcomes.
Probability = favorable outcomes / total possibilities
P(diamond) = 13/26 = 1/2
|
test/551418: -3x + 4y= 8
x +2y =10
1 solutions
Answer 359722 by oberobic(2304) on 2012-01-01 14:25:48 (Show Source):
You can put this solution on YOUR website!-3x + 4y = 8
x + 2y = 10
.
Multiply the second equation by 2 and then subtract the second equation to eliminate the 'y' term.
.
-3x +4y = 8
2x + 4y = 20
------------- subtract
-5x = -12
x = -12/-5 = 12/5
.
Now substitute to find 'y' using the first equation.
.
-3*(12/5) + 4*y = 8
4y = 8 +36/5 = 40/5 + 36/5 = 76/5
y = 19/5
.
Check these values using the second equation to be sure this is the answer.
(12/5) + 2*(19/5) = 10
12/5 + 38/5 = 50/5 = 10
Correct.
.
Answer: x = 12/5, y = 19/5, which can be shown as the ordered point (12/5, 19/5).
.
Done.
|
Word_Problems_With_Coins/551078: The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange and each apple. Can u please help me solve this??!
1 solutions
Answer 359352 by oberobic(2304) on 2011-12-30 11:54:18 (Show Source):
You can put this solution on YOUR website!x = price of oranges
y = price of apples
.
12x + 7y = $5.36 = 536 cents
8x + 5y = $3.68 = 368 cents
.
Multiply the first equation by 5, the second by 7, and then subtract to eliminate the 'y' factor.
.
60x + 35y = 2680
56x + 35y = 2576
----------------- subtract
4x = 104
x = 26 cents per orange
.
Substitute x=26 into the first equation to find 'y'.
.
12*26 +7y = 536
312 +7y = 536
7y = 536-312 = 224
y = 32 cents per apple
.
Check these values using the other equation.
8*26 = 208 cents
5*32 = 160 cents
208+160 = 368 cents
Correct.
.
Answer: Oranges cost 26 cents each; apples cost 32 cents each.
.
Done.
|
Graphs/551050: graph of y=2x +4. Then graph the equation to check your answer y=3x-9
1 solutions
Answer 359348 by oberobic(2304) on 2011-12-30 11:29:08 (Show Source):
You can put this solution on YOUR website!The lines will cross where:
2x + 4 = 3x -9
-x = -13
x = 13
.
y = 2*13 + 4 = 30
y = 3*13 - 9 = 30
.
The red line is y = 2x+4.
The green line is y = 3x-9.
They intersect at (13,30).
.
|
Coordinate-system/551069: OK im suppose to rewrite this equation to find out how many solutions it has, but my problem is that i dont know if im suppose to add or subract. x+y=-3 x+y=3
1 solutions
Answer 359342 by oberobic(2304) on 2011-12-30 10:49:41 (Show Source):
|
Word_Problems_With_Coins/551039: if the number of dimes are 4 less than 5 times the quarter find how many of each type does he have
and the total is $1.85
1 solutions
Answer 359341 by oberobic(2304) on 2011-12-30 10:47:18 (Show Source):
You can put this solution on YOUR website!d = number of dimes
10d = value of dimes in cents
q = number of quarters
25q = value of quarters in cents
.
The number of dimes is 4 less than 5 times the number of quarters.
d = 5*q -4
.
10d + 25q = 185 cents
.
Substitute
.
10*(5q-4) + 25q = 185
.
50q -40 +25q = 185
.
75q = 225
.
q = 3
.
d = 5*3-4 = 11
.
Check the values.
25*3 = 75 cents
11*10 = 110 cents
75+110 = 185 cents
Correct.
.
Answer: 3 quarters and 11 dimes.
.
Done.
|
Angles/551056: one of two supplementary angles is 30 degrees greater than twice the other. find the degree measure of each angle?
1 solutions
Answer 359340 by oberobic(2304) on 2011-12-30 10:37:35 (Show Source):
You can put this solution on YOUR website!Two angles can be defined as 'a' and 'b'.
They are supplementary, so: a+b=180.
a = 2*b +30
Substitute
2b + 30 +b = 180
3b = 150
b = 50
a = 2*50 + 30 = 130
or
a = 180-50 = 130
.
Answer: The two angles are 50 degrees and 130 degrees.
.
Done.
|
Mixture_Word_Problems/551060: A chemist wants to make a 10% solution of fertilizer. How much water and how much of a 30% solution should the chemist mix to get 30L of a 10% solution?
1 solutions
Answer 359338 by oberobic(2304) on 2011-12-30 10:29:25 (Show Source):
You can put this solution on YOUR website!The key consideration with mixture problems is how much 'pure' stuff you need.
The chemist wants 30 liters of a 10% solution: 30 * .1 = 3 liters of pure fertilizer and 27 liters of water.
He has 30% solution on hand.
.
x = liters of 30% solution
.
30-x = liters of water to add, which is 0% pure fertilizer
.
.3*x + 0*(30-x) = .1*30
.
.3x = 3
.
x = 10 liters of 30% solution
.
30-x = 20 liters of pure water
.
Done.
|
real-numbers/551051: The driving distance between Pensacola and Key West is 792 miles. Bus A leaves Pensacola at 6:00 a.m. traveling at an average 42 miles per hour. Bus B leaves Key West at 7:00 a.m. traveling at an average speed of 33 miles per hour. At what distance, in miles, from Key West will the two buses meet?
This question has me confused so please help me with this.
1 solutions
Answer 359327 by oberobic(2304) on 2011-12-30 08:33:36 (Show Source):
You can put this solution on YOUR website!The buses are converging at their combined speed: 42+33 = 75 miles/hr.
When they meet, they will have covered the entire distance: 792 miles.
The fundamental distance equation is: d = r*t
We know 'd' and 'r', so we can solve for 't'.
t = 792 miles / 75 miles/hr = 10.56 hr.
.56 hr * 60 min/hr = 33.6 min.
.
We now have to arrange these facts to answer the question: How far from Key West will they be?
.
Well, the bus that left Key West was going 42 mph * 10.56 hr = 443.52 miles.
.
We can check the distance based on leaving Pensacola.
That bus traveled 33 mph * 10.56 hr = 348.48.
That is how far from Pensacola they are. We know the distance from Pensacola to Key West is 792,
so the bus is 792 - 348.48 = 443.52.
That's confirms the answer since it matches the other distance.
.
Answer: The buses are 443.52 miles from Key West when they meet.
.
Done.
|
Quadratic_Equations/551052: find k so thqqt the equation x2-11x+k=0 andx2-14x+2k=0 may have a common root
1 solutions
Answer 359325 by oberobic(2304) on 2011-12-30 08:25:14 (Show Source):
You can put this solution on YOUR website!f(x) = x^2 -11x + k
g(x) = x^2 -14x + 2k
.
x = 0 defines the roots
But that reveals we would be looking for a point where k = 2k.
That exists only at k=0.
Given k=0, we can redefine f(x) and g(x):
f(x) = x*(x-11)
g(x) = x*(x-14)
They share the common root 0.
.
|
Linear_Algebra/550939: The line through the point (-2, 6) with
slope -5 is ?
another problem :
A line parallel to y=8x-1 is?
Another Problems :
Find the slope of the line through the
points (-8, 5) and (-23, 2).
1 solutions
Answer 359278 by oberobic(2304) on 2011-12-30 00:28:28 (Show Source):
You can put this solution on YOUR website!y = -5x + b
Use the point (-2,6) to find 'b'.
6 = -5*-2 + b
6 = 10 + b
-4 = b
y = -5x -4
.
A line parallel to y = 8x-1 is any line with slope = 8, for example.
y = 8x +1
.
m = (5-2)/(-8-(-23)) = 3/(-8+23) = 3/15 = 1/5
.
Done.
|
Geometry_Word_Problems/550977: A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. How long are the legs of the triangle?
1 solutions
Answer 359276 by oberobic(2304) on 2011-12-30 00:21:33 (Show Source):
You can put this solution on YOUR website!Use the Pythagorean Theorem.
c^2 = 10^2 = 100
c^2 = a^2 + b^2
a = b
100 = a^2 + a^2 = 2*a^2
a^2 = 50
a = sqrt(50) = sqrt(25*2) = 5*sqrt(2)
so,
The legs are each 5*sqrt(2) inches.
|
Rectangles/550966: a rectangle has a perimeter of 96 cm .its length is twice its breadth. find its dimensions.
1 solutions
Answer 359273 by oberobic(2304) on 2011-12-30 00:14:04 (Show Source):
You can put this solution on YOUR website!p = 2(l+w), where p=perimeter, l=length, and w=width.
p = 96 cm, given
l = 2*w, given
96 = 2(2*w + w) = 4w + 2w = 6w
6w = 96
w = 16
l = 2*w = 32
.
check the perimeter
2*(16+32) = 2*48 = 96
correct.
.
Answer: length = 32 cm and width = 16 cm
.
Done.
|
|
