Questions on Word Problems: Evaluation, Substitution answered by real tutors!

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Solution A
Amount = x
Concentration = 55%=0.55
Solution B
Amount = 400-x
Concentration = 25%=0.25
Resultant Solution
Amount = 400
Concentration = 40% =0.4


(Amount of A)(concentration of A)+ (Amount of B)(concentration of B)= (Amount of resultant)(concentration of resultant)
(x)(0.55)+(400-x)(0.25)=(400)(0.4)
0.55x+100-0.25x=160
0.55x-0.25x=160-100
0.3x=60
0.3x/0.3=60/0.3
x=200

200ml of a 55% acid solution must be mixed with a 200ml of 25% solution to produce 400 mL of a 40% solution

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What quantity of a 55% acid solution must be mixed with a 25% solution to produce 400 mL of a 40% solution?
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40% is the average of 55% and 25%, so it's equal amounts.

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Let's say that the first three numbers are: a, b, and c. We need to find their sum.
"The average of the first three numbers was 42".
So the sum of the first three numbers is
The next seven numbers we'll identify as: d, e, f, g, h, i, j and their average is:
"The average of the next seven numbers was only 12". So their sum is
So we have 10 numbers altogether. To find their average, divide their sum by the number of numbers (that's 10):
=
The average of all ten numbers is 21.

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lower limit:


ohms
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upper limit:


ohms

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The sum of two numbers is twelve. Four less than three times the smaller is equal to the larger. find the smallest and largest number?
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Equations:
x + y = 12
x = 3y-4
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Substitute and solve for "y":
3y-4+y = 12
4y = 16
y = 4 (smaller)
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Solve for "x":
x = 3y-4
x = 12-4 = 8 (larger)
=================
Cheers,
Stan H.

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"For a mathematics project, 26 students were divided into four groups.
G1 + G2 + G3 + G4 = 26
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Two groups had the same number of student.
Let G1 and G2 have "x" students.
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The other two groups each had one more student than the smaller groups.
Then G3 and G4 must have "x+1" students.
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How many students were in the smaller group?"
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Equation:
x + x + x+1 + x+1 = 26
4x + 2 = 26
4x = 24
x = 6 (# of students in the smaller group).
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also..
"When she graduated fom college, Regina was offered two jobs.
One paid a starting salary of $30,000 annually, plus guaranteed increases of $2,000 per year.
S1 = 30000 + 2000x for x = 1,2,3...
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The other paid a starting salary of $25,000 annually, plus guaranteed increases of $3,000 per year.
S2 = 25000 + 3000x for x = 1,2,3...
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After how many years would the salaries be equal?"
Equation:
Solve: S1 = S2
30000 + 2000x = 25000 + 3000x
1000x = 5000
x = 5 years
================
Cheers,
Stan H.

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suppose x = t^2 + t and y = t^3 + t^2. if x = 2 what are the two possible values of y.
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If x = 2, we can solve for t:
t^2 + t = 2
t^2 + t - 2 = 0
Factor:
(t+2)(t-1) = 0
This gives t = -2, 1
So the possible values for y are:
(-2)^3 + (-2)^2 = -4
1 + 1 = 2
Ans: -4, 2

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2 cc

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The perimeter of a rectangle is 66m
the length is 1 m more than three times the width
find the dimensions of the rectangle
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Perimeter = 2(width + length)
66 = 2(w + 3w+1)
33 = 4w+1
4w = 32
width = 8 m
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length = 3w+1 = 25 m
===========================
cheers,
Stan H.
==============

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The product of two numbers is 42. The difference of the same two numbers is 11. What are the two numbers
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Factor 42
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1*42
2*21
3*14
6*7

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Are we assuming the 24 people are splitting the money equally? If so, each person gets $8,808,000/24=$367,000. But of course we have to subtract the money each person put into the pool (you didn't provide that information, though). And, unfortunately, each person would only get about half that amount after taxes.

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suppose a ball is thrown vertically up in the air so that the height of the ball after t seconds is s(t)=80t-16t^2. What is the height of the ball after 1 second?
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s(t)=80t-16t^2
Sub 1 for t

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Use algebra.

20 + .32x = 35 + .20x | subtract .20x from both sides and subtract 20 from both sides.

20 + .32x -.20x -20 = 35 + .20x -.20x -20
.12x=15 |divide both sides by .12
x = 125

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This is exactly the same as a "two kinds of coins in a pig bank" problem. You have to derive an equation that relates to the total NUMBER of the two things and then an equation that relates to the total VALUE of the two things. In this case, the value is expressed in points, but the idea and the process are the same.

Let represent the number of 8 point questions and represent the number of 10 point questions. Then the point value of all of the 8 point questions is and the point value of all of the 10 point questions is . The total NUMBER of questions is 21 and the total point VALUE of all the questions is 200, so:





Just solve the 2X2 linear system.

John

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

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As mentioned the diomensions are 100 times for real building as compared to mentioned in model so if the model is x cm and then real real building will be 100x cm.

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There was a misunderstanding with the previous answer. For the question, A, B, C & D represent 4 different numbers and the multiplication of number AB with number CD results in a number DDD.

The key to solving this problem is to recognize that DDD has factors of D and 111.
In turn, 111 has factors 3 and 37.

Stop reading now as you may be able to solve with that clue.



Did you get it?

To continue (DDD) = (37 * 3 * D ) = (AB * CD)
Thus can infer that either AB or CD is 37 and the other number is D * 3.
Using guess and check to find D and we get 5 and 7 as possible value of D.
So, ensuring that the digit value of the second number is D ...
D=5:
37 * 3 * 5 = 555
37 * 15 = 555
A=3, B=7, C=1, D=5
and
D=7:
37 * 3 * 7 = 777
21 * 37 = 777
A=2, B=1, C=3, D=7

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score is 81 on verbal and 6.4 on quantitative.
mean for verbal is 50 and standard deviation is 20.
mean for quantitative ability is 0 and standard deviation is 5.
strongest would be how the person does relative to the other people.
when the mean is 50 and the standard deviation is 20, then a score of 81 would be equal to (81-50)/20 = 1.55 standard deviations above the mean.
when the mean is 0 and the standard deviation is 5, then a score of 64 would be equal to (6.4-0)/5 = 1.28 standard deviations above the mean.
this person's stronger ability is verbal.
what i calculated was the person's z-score for each of the tests.
the higher the z-score, the more people have a score less than that and the less people have a score greater than that.
if your were able to look up the z-score in a table, you would find that:
with a z-score of 1.55, 94% of the people taking the test would have scores less than that and only 6% would have scores greater than that.
with a z-score of 1.28, 90% of the people taking the test would have scores less than that and only 10% would have scores greater than that.
he did good in both tests, but he scored better than the general population in the test of verbal ability.

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number of students = 800
number of faculty members = 50
number of administrators = 150
total = 1000
assuming the selection was random, then:
probability it would be a student would be 800 / 1000
probability it would be a faculty member would be 50 / 1000
probability it would be an administrator would be 150 / 1000
probability it would be a faculty member or an administrator would be 200 / 1000
probability it would be anyone except an administrator would be 850 / 1000
the probability it would be any number of a certain type is the number of occurrences of that type divided by the number of total occurrences.
in the case of the faculty member or administrator, this assumes that a person is not a faculty member and an administrator at the same time.
the generic term for this is that each type is mutually exclusive which means that you can't have a member of one type being also a member of the other type.

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18/0.60=$30

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On three consecutives passes, a football team gains 5 yards, loses 10 yards and gains 45 yards. What number represents the total net yardage?
The answer I got was 5-10+45=50
The answer you should have is = 40 yds
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- Solve by using the substitution method. 8x+3y=-42 and x=8-7y
Substitute for "x" and solve for "y":
8(8-7y) + 3y = -42
64-56y + 3y = -42
-53y = -106
y = 2
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Solve for "x":
x = 8-7y
x = 8-7*2 = -6
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-What is the domain of
p(x)=x^2-2x+1
Domain is "All Real Numbers".
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y= (6/5)x+5
Domain is "All Real Numbers".
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Determine if (-1,6) is a solution for 6x-6y=1
Check: 6*-1-6*6 = 1
-6-36 = 1
No, (-1,6) is not a solution.
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Find the slope for (3,9) and (7-10)
slope = (9--10)/(3-7) = 19/-4 = -19/4
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Find the slope and the y-intercept for f(x)=-2x-3
Slope = -2
y-intercept = -3
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Solve 7x not equal to 35
Divide both sides by 7 to get:
x # 5
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Cheers,
Stan H.
==============================

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there are cows and chickens on the barnyard and there are 24 legs. how many cows? how many chickens? how do you know?
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2ch + 4cow = 24
There's more than 1 answer, no unique solution.
0 chic and 6 cows
2 chic and 5 cows
4 chic and 4 cows etc

[I suppose near his bong collection J!
About two years ago, Michael was photographed smoking weed in a bong 
here in my hometown of Columbia SC!

We only need the first 2 clues. The last two are irrelevant.

If 4 is on B, then 6 is not on B by clue i)
So where is 6? Either A or C. But 6 can't be on A 
because clue ii) says 1 must be on the shelf above 6,
but there is no shelf above A. So 6 must be on C, and
by clue ii) 1 is above it on B.  So the answer is 1.

Edwin