# Questions on Algebra: Average answered by real tutors!

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Question 994722: Hello, I am in need of help. I have this problem on an optional assignment, and I cannot seem to figure it out. I do not know if this is the right department/topic area, but I will assume so. The problem is:
The average of 3 numbers is 22
The average of 2 numbers is 21.5
What is the third number?
The wording somewhat confuses me, and I cannot seem to find the solution. If you could help me, I would be very grateful. I also would want to see how I would solve this for future reference, if possible. Thank you so much!

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
A,B, and C are the three numbers.
.
(A+B)/2=21.5
A+B=43 . Use this to Substitute for A+B below
.
(A+B+C)/3=22
A+B+C=66 Substitute for A+B from above
43+C=66
C=23
.
ANSWER: The third number is 23.

Question 994660: The average of four numbers is 67 three of these numbers are 67 87 72 what is the fourth number
Found 2 solutions by macston, stanbon:
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
A=average; F=fourth number
.
A=(sum of numbers)/(how many numbers)
.
67=(67+87+72+F)/4
.
268=226+F
.
42=F
.
ANSWER: The fourth number is 42.

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
The average of four numbers is 67 three of these numbers are 67 87 72 what is the fourth number
----
Let the 4th number be "x".
Equation:
(67+87+72+x)/4 = 67
----------
x + 226 = 268
---
x = 42
------------
Cheers,
Stan H.
----------------

Question 994096: To get a 85% or above average in my overall grade/report card, what grades do I need to have for each of my 6 (maybe 7 I'm not sure) classes to make sure my overall average is again, an 85% or above? Please answer asap, thank you.
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

The sum of your grades must be greater than or equal to 6 (or maybe 7) times 85.
John

My calculator said it, I believe it, that settles it

Question 994008: a man runs to a telephone booth and comes back in 15 minutes. his speed on the way to tha booth is 5m/s and his speed on tha way back is 4m/s. find the distance to the telephone booth
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
a man runs to a telephone booth and comes back in 15 minutes. his speed on the way to tha booth is 5m/s and his speed on tha way back is 4m/s. find the distance to the telephone booth
------------
To the booth DATA:
rate = 5 m/s ; distance = x meters ; time = d/r = x/5 meters/second
------
From the booth DATA:
rate = 4 m/s ; distance = x meters ; time = d/r = x/4 meters/second
-----
Equation:
time + time = 900 seconds
-----------
x/5 + x/4 = 900
4x + 5x = 20*900
9x = 20*900
x = 2000 meters
----------
Cheers,
Stan H.

Question 993892: I've lost my mind and can't solve for 100%.
I know that 88% = 2416669 but i need to show to solve for 100% and what is 100% and i get it in my mind and can't figure it out.

Answer by macston(4006)   (Show Source):
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x=100%
0.80x=2416669
x=2416669/0.80
x=3020836.25

Question 993854: The average score for a class of 25 students was 75. If the 15 female students in the class averaged 70, then the male students in the class averaged:
a. 85.0
b. 70.0
c. 82.5
d. 77.5
e. 75.0

Answer by Theo(5548)   (Show Source):
You can put this solution on YOUR website!
if the average score for the 25 students was 75, then the total score for all students had to be 25 * 75 = 1875.

if the average score for the 15 female students was 70, then the total score for the female students had to be 15 * 70 = 1050.

the total score for the male students had to be 1875 - 1050 = 825.

since there were 10 male students, then their average score had to be 825 / 10 = 82.5.

that should be selection c.

Question 993774: If a giraffe runs for 30 minutes at a speed of 40 miles per hour, how far will the giraffe run?
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
If a giraffe runs for 30 minutes at a speed of 40 miles per hour,
how far will the giraffe run?
____
distance = (rate)*(time)
----
Ans: D = (40 mph)(1/2 hr) = 20 miles
-------------------
Cheers,
Stan H.
----------

Question 993459: What is four fifth plus one third
Answer by macston(4006)   (Show Source):

Question 993397: If the average of six numbers is 12, and two of those numbers are 5 and 11, what is the average of the other four numbers?

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
(6)(12)=72
The sum of the six numbers is 72.
Subtracting 5 and 11, the sum of the 4 remaining numbers is 72-16=46
The average of 4 numbers whose sum is 46 is 46/4=11.5
.
ANSWER: The average of the other 4 numbers is 11.5.

Question 993244: What is the average for 100,21,46

You can put this solution on YOUR website!
Their average is the sum of their values, 100+21+46, divided by their numbers, in this case 3. Using your calculator, add the values and divide by 3 to find your answer.

Question 993149: Sue’s scores on five tests are 84, 80, 76, 96, and 80. What must Sue score on the sixth test so that her average will
be 85? State your variable, set up an equation and solve the equation.

Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
For Sue to attain an 85 average,
the total of her scores must equal
=> 85 x 6 = 510
Adding up her 5 scores:
84 + 80 + 76 + 96 + 80
= 416
510 - 416 = 94
Sue must score 94 on her 6th test
to get an 85 average.
Hope this helps :-)

Question 993045: A man traveled at 60 kph for 2hours and at 51 kph for 11/2hours. What was the average speed for the journey to the nearest kilometer pef hour (kph) ?
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Find the total distance.
Divide it by the total hours.

Question 992883: Six test scores are given. The first five test scores are 15% of the final grade and the last test score is 25% of the final grade. Find the weighted mean of the test score .
Test scores: 65 72 84 89 70 90

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Six test scores are given. The first five test scores are 15% of the final grade and the last test score is 25% of the final grade. Find the weighted mean of the test score .
Test scores: 65 72 84 89 70 90
--------
0.15(65+72+84+89+70)+0.25*90 = 57+22.5 = 79.5
-----------
Cheers,
Stan H.
---------

Question 992680: A person is trying to lose weight and they have a goal to lose 30 pounds. So far, that person has lost 15 pounds, which is 10% of their weight. What is the persons original weight?
Answer by Theo(5548)   (Show Source):
You can put this solution on YOUR website!
if he lost 15 pounds, and that represents 10% of their original weight, then the person's original weight is equal to 15 / .10 = 150 pounds.

assuming 150 pounds original weight, then 15 is equal to 15/150 = .10 * 100 = 10%.

Question 992727: Why does geometric mean and arithmetic mean give different answers
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
It is because the arithmetic mean and geometric mean are really different means.

See the lesson  Difference between Arithmetic mean and Geometric mean  in this site,  may be it will help.

See also two more lessons in this site
- Arithmetic mean and geometric mean inequality and
- Arithmetic mean and geometric mean inequality - Geometric interpretations
if you really want to know more about these means.

Question 992291: A car rental company offers two plans for renting a car.
Plan A: 38 dollars per day and 20 cents per mile.
Plan B: 57.04 dollars per day and 12 cents per mile.
If you plan to rent the car for one day, and m represents the number of miles driven in that day, for how many miles driven would you save money with plan B?

Answer by Theo(5548)   (Show Source):
You can put this solution on YOUR website!
equation for plan A is ca = 38 + .20 * x
equation for plan B is cb = 57.04 + .12 * x

question is for how many miles driven would you save money with plan B.

you will save money with plan B when the cost of plan B is less than the cost of plan A.

this means that cb < ca

replace cb with it's equation and replace ca with its equation to get:

57.04 + .12 * x < 38 + .20 * x

subtract 38 from both sides of this equation and subtract .12 * x from both sides of this equation to get:

57.04 - 38 < .20 * x - .12 * x

combine like terms to get:

19.04 < .08 * x

divide both sides of this equation by .08 to get:

19.04 / .08 < x

238 < x

solve for x to get x > 238 miles.

when x = 238 miles, plan A costs 85.6 and plan B costs 85.6.
plan B costs the same as plan A.
this is the break even point.

when x = 239 which is greater than 238, plan A costs 85.8 and plan B costs 85.72.
plan B is now cheaper than plan A and will remain cheaper as long as the number of miles driven is greater than 238.

Question 992312: After five exams, Andrew has a mean mark of 70.
What mark must he get in the next exam to raise
his average to 72?

Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
After five exams, Andrew has a mean mark of 70.
What mark must he get in the next exam to raise his average to 72?
:
let x = the mark of the 6th exam
= 72
= 72
multiply both sides by 6
350 + x = 6(72)
subtract 350 from both sides
x = 432 - 350
x = 82 is the grade must get to raise his average to 72

Question 992290: Joe has scored 87, 92, and 82 on his first three exams in his math class. If the standard 70,80,90 scale is used for grades and the exams are equally weighted, what must he score on the final exam, f, in order to
a) Get a C average on exams?
b) Get a B average on exams?
c) Get an A average on exams?

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

If you have scores and need to know the score on the th assignment in order to have an average of , then multiply times and subtract the sum of the first scores.

John

My calculator said it, I believe it, that settles it

Question 992136: The average age of 54 girls in a class was
calculated as 14 years. It was later realized that the
actual age of one of the girls in the class was
calculated as 13 years. What is the actual average
age of the girls in the class?

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
The average age of 54 girls in a class was
calculated as 14 years. It was later realized that the
actual age of one of the girls in the class was
calculated as 13 years. What is the actual average
age of the girls in the class?
===================
More than 1 girl could be 13.
Makes no sense.

Question 992046: If there are 4 quizzes and each quiz is 100 points, you must get a total of at least 320 points overall on your quizzes to receive a B.If your scores are 85,68, and 90, what is the range of scores you can get on the last test that will give you an overall B?
Answer by hovuquocan1997(82)   (Show Source):
You can put this solution on YOUR website!
Your scores for the first three quizzes are 85, 68, 90, so the total points you have so far is:
points
You need at least 320 points, and now you only have 243 points, that means on the last test, you have to get at least 77 points because

So the range of scores you can get on the last quiz that will give you an overall B is from 77 to 100
I hope this answer is helpful :)

Question 991396: In your Economics I class there are four tests and a final exam, all of which count equally. Your four test grades are 96, 87, 80, and 92. What grade on your exam is needed so your average is between 80 and 90 for the course?
Let x represent your score on the exam.

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Multiply 80 by 5. From that, subtract the sum of the scores you already have. The result is the lowest score you can obtain and have a score of 80 or better.

Multiply 90 by 5. From that, subtract the sum of the scores you already have. The result is the largest score you can obtain and have a score of 90 or less.

John

My calculator said it, I believe it, that settles it

Question 991051: Given the function f(x)=5x^2+5x+4, find the following quantity if it exists.
f(x−5)−f(x)=

Answer by Fombitz(25151)   (Show Source):

Question 991049: Let r(x)=(2x-9)/9x+3. Find and simplify
r^−1(x)=?

Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!
Use x and y.

Interchange x and y and solve for the new y.
That new y is the inverse.

Question 991110: Monica has tests score of 76, 90, 94 and 88. What does she need on the final exam in order to have an average score of 90?

Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!

Now solve for F.

Question 991050: Given the functions f(x)=x^2+6 and g(x)=√(x+1), find the following quantity if it exists.
(f∘g)(−5)=

Answer by MathLover1(11324)   (Show Source):

Question 990785: Sam has scored a 70%, 85%, 94%, and an unknown score on his fourth test. Find an expression that explains what Sam has to get on his 5th test to have a test average of 90%.
Thank you.

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
The sum of 5 grades to average 90 is (5)(90)=450
Let x=4th score and y=5th score
450-70-85-94-x-y=0
201-x=y
.
Sam must get a score of (201-his fourth score)
on his fifth test to average 90.
(He must average more than 100% on tests 4 and 5).
.

Question 990795: Four prime numbers are arranged in ascending order. The product of first three is 385 and that of last three is 1001. The largest prime number is?
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Four prime numbers are arranged in ascending order. The product of first three is 385 and that of last three is 1001. The largest prime number is
-----------
Factor 1001.

Question 990637: The average of squares of first 11 consecutive even numbers?
Hear answer is 184.How it possible?

Answer by farohw(153)   (Show Source):
You can put this solution on YOUR website!

Formula:
Let n = 11.

= 184.

Question 990633: Rahul average goes by 1 after scoring 21. His average goes by 2 more after the next score of 35. what is the total runs scored by rahul including 21 and 35 ?
Answer by anand429(129)   (Show Source):
You can put this solution on YOUR website!
Let total runs scored before = x
No of innings = y
Avg. = x/y
After scoring 21,
Avg. = (x+21)/(y+1) which should be equal to (x/y) + 1
or,
=>
=>
=> ------------------------(i)
Similarly,

=>
=> -----------------------(ii)
Multiplying (i) by 2, we get,
------------------------(iii)
Subtracting (iii) from (ii)

=> y = 10 (Since y can not be 0)
Putting in (i)
100-200 + x = 0
=> x = 100
So runs scored including 21 and 35 = 100 +21 +35 = 156

Question 990417: Jake's average score on the first for math tests is 83. On his first test he scored a 72 and his second test he scored an 81. On his fourth test he scored on more point then he did on his third test. What was the score of Jake's fourth math test?
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Make his third test = 'x'
Fourth test then = x + 1
So adding up the 4 tests
(83 + 72 + x + (x + 1))/4 = 83
Totalling up.
(2x + 156)/4 = 83
(2x + 156) = 83 x 4
2x + 156 = 332
2x = 332 - 156
2x = 176
x = 88
4 scores are:
83,72,88,89.
So, fourth score was 89.
Hope this helps :-)

Question 990326: Determine the average rate of change of the function between the given values of the variable.
g(x)= 5/x+9
x=0, x=h

Answer by KMST(3791)   (Show Source):
You can put this solution on YOUR website!
I assume that you meant = 5/(x+9) ,
because = 5/x+9 is undefined for .

The average rate of change of the function between to is
,
the change in the value of the function,
divided by the corresponding change of the variable.
The values of the function are:
for , ,
for , .
As the value of changes by units from to ,
the value of changes by
.
The average rate of change of the function between to is

Question 990440: Hey question if I got 82% on my last two exams what do I need on my third exam to pass with a 75%....I'm really bad at math I got 41/50 on 2 tests & 31/50 on my 3rd test what is my overall grade ? I did 41+41+31=113 then I did 113/150 & it gave me 0.7533 does that mean I got a 75%?
Answer by Boreal(1464)   (Show Source):
You can put this solution on YOUR website!
Yes, 0.7533 is 75.33%. Move the decimal two places to the right.
Remember it by using 0.5000=50.00%.

Question 990421: what are 2 numbers that would make an average of 92

Found 2 solutions by macston, Alan3354:
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
F=first number; S=second number
.
F+S=2(92)
F+S=184
S=184-F
.
Pick any number (first number), F.
Subtract F from 184 to get S.
F and S are two numbers that average 92.
EXAMPLE:
Pick the number 10.
First number is 10.
Second number=184-first=184-10=174
The two numbers are 10 and 174
.
Find the average:
(10+174)/2=92
184/2=92
92=92

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Any 2 numbers with a sum of 184.
n1 = 184 - n2
Pick any number for n2, find n1.

Question 990418:

Multiple choice: A debate team has 15 female members.
The ratio of females to males is 3:2. How many males are on the
debate team?

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
M=males on team
.

.
ANSWER: There are 10 males on the team.

Question 990327: Determine the average rate of change of the function between the given values of the variable.
g(x)= 5/x+9
x=0, x=h
I really need help :/

Found 2 solutions by Boreal, stanbon:
Answer by Boreal(1464)   (Show Source):
You can put this solution on YOUR website!
g(x)=5/(x+9)
that is between (5/9) and (5/h+9)
subtract the first from the second and divide by h.
(5/h+9)-(5/9)={1/9(h+9)}*-5(h+9)+45;
the numerator is -5h-45+45=-5h
the denominator is 9(h+9)
The difference is -(5/9) (h/h+9);
I still have to divide by h to get the average over the interval 0 to h.
That is -5/9(h+9).
===
with calculus, the first derivative is -5/(x+9)^2
evaluated at 0, it is -5/81
evaluated at h, it is -5/9(h+9), and as h goes to 0, the result is-5/81

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Determine the average rate of change of the function between the given values of the variable.
g(x)= 5/x+9
x=0, x=h
----
Note: Average rate = (change in y)/(change in x)
-------
Ans: Ave rate = [g(h)-g(0)]/(h-0)
---
= [5/(h+9)-(5/9)]/h
----
= (5/h)[9-(h+9)]/[9*(h+9)]
----
= -5/[9(h+9)]
-----------
Cheers,
Stan H.
------------

Question 990248: Xavier is taking a geology course in which four tests are given. To get a B, he must average at least 80 on the four tests. He got scores of 82,76, and 78 on the first three test. Determine what scores on the last test will allow him to get at least a B
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
Let x=score on final test
To average at least 80:
(82+76+78+x)/4 => 80
(236+x)/4=>80
236+x=>320
x=>84
.
ANSWER: He must score at least 84 to average 80 .

Question 990059: if a teacher has less than 80 students in a class and decided to put them in group of 14 she would have 3 not in a group.if she decided put 16 in a group she would have 9 not in a group. how many children does she have in the class
Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
if a teacher has less than 80 students in a class and decided to put them in group of 14 she would have 3 not in a group.
if she decided put 16 in a group she would have 9 not in a group. how many children does she have in the class
:
find the multiples of 14 plus 3
17, 31, 45, 59, 73
Find the multiples of 16 plus 9
25, 41, 57, 73,
:
73 is the only one common to both groups; 73 students
:
5 groups of 14 with 3 left over
4 groups of 16 with 9 left over

Question 989915: While still in the hospital, the doctor writes an order for an antibiotic at 3mg/kg/day. You are nervous now because the nurse was wrong before. Assuming that you weigh 123lbs., determine how many milligrams you should be given. Then convert the number of milligrams to be given to the correct number of grams. (Hint: 1000mg=1g and mg/kg/day= mg
------
kg * day

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!

milligrams per day

Question 989914: When you don’t seem to be getting any better, you eventually end up in the hospital. The doctor orders 120mg of medicine to be given twice a day. The nurse comes in with 6 tablets and tells you that they are 30mg each tablet. Is this the correct dosage? If not, how many tablets should you get?
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
" 6 tablets and tells you that they are 30mg each tablet"
6*30 = 180 mg total

but you need 120*2 = 240 mg total. So the dosage is short. You need 240/30 = 8 tablets instead of 6. The 8 tablets will be divided into 2 groups, since you take the medicine twice a day, so 8/2 = 4 tablets per session.

Question 989672: Identify a pattern and find the next three numbers in the pattern.
1,3,9,27,81....

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Identify a pattern and find the next three numbers in the pattern.
1,3,9,27,81, 3^5 = 243, 3^6 = 729, 3^7 = 2187....
-------
Cheers,
Stan H.
-------------

Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
Each previous term is being multiplied by 3 to get the next term

1*3 = 3
3*3 = 9
9*3 = 27
27*3 = 81
etc etc

The next three numbers would be

81*3 = 243
243*3 = 729
729*3 = 2187

Question 989505: Paula and Melinda are considering selling their house, which they paid $150,000 for, but they'll only do so if they make at least a 10% profit. They'll have to pay 7% of the selling price in commission to their real estate agent, as well as$1,000 in closing costs. A potential buyer has offered $163,000 for the home. How much will they need to raise that offer for Paula and Melinda to consider accepting it? Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! 10% profit is 15,000 which takes the price to 165,000. Then add 1,000 to cover the closing costs;$166,000. Then multiply by 1.07 to cover the commission.

John

My calculator said it, I believe it, that settles it