# Questions on Algebra: Proportions answered by real tutors!

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 Algebra: Proportions Solvers Lessons Answers archive Quiz In Depth

Question 751177: Solve 3/5+m/24 I missed alot of school & idk how to do these problems
Found 2 solutions by Edwin McCravy, timvanswearingen:
Answer by Edwin McCravy(8908)   (Show Source):
You can put this solution on YOUR website!
The other tutor though you meant "solve the equation"
when you actually meant "simplify the expression",
or "add (or combine) the fractions".

We want to turn those two added fractions into just
one single fraction:

Those two fractions have different denominators.
Before we can add them, they have to have the same
denominators.  So we change them so they will have
the same common denominator.

The two different denominators are 5 and 24.
Since there is no whole number except 1 that goes
into both of them, we can find the LCD by multiplying
them together: 5×24 = 120.  That's the LCD.

To make the denominator 5 become the denominator
120 we multiply top and bottom of that fraction by 24.

To make the denominator 24 become the denominator
120 we  multiply top and bottom by 5.

We do both of those

That becomes:

Now we indicate the addition of the numerators over
the common denominator 120:

That's the final answer because now there is only one
fraction.

Edwin

You can put this solution on YOUR website!
You need to rewrite the question. I think you forgot to say what it was equal to. Just respond to this with the question written correctly and I'll help you out.

Question 751049: An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 6861 fur seal pups were tagged in early August. In late August, a sample of 600 pups was observed, and 219 of these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.
The estimated total number of fur seal pups in Rookery A is ____. (Round to the nearest whole number.)
Additional instructions: Set up a proportion, and then use the cross products principle of proportions. If a/b=c/d, then ad=bc. Be sure to round to the nearest whole number.

You can put this solution on YOUR website!
Late august----------- 600 observed : 219 tagged
Early august--------- p whole population : 6861 tagged

After the 6861 pups tagged in early august were released, they mixed uniformly with the whole seal population. The result of this mixing was as found in late august, but those 600 observed in late august gave a ratio which would be a strong estimate of the true ratio; no matter, we would setup the proportion using these ratios.
We want to find p, the whole population.

.
for best accuracy because we only have up to three significant figures.

Question 749784: The ratio of AB: BC is 3:2. If AC=15 cm, find the length of AB
You can put this solution on YOUR website!
The ratio of AB: BC is 3:2. If AC=15 cm, find the length of AB
-----
AB = 3x
BC = 2x
---
Equation:
3x + 2x = 15
5x = 15
x = 3
----
AB = 3x = 3*3 = 9
=====================
Cheers,
Stan H.
==================

Question 749529:
Two trains were 332 miles apart and heading towards each other at 11 am. If the trains meet at 1 pm and one train was traveling 36 miles per hour faster than the other, then how fast was each train moving?

Found 2 solutions by checkley79, josmiceli:
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D=RT
332=R*3
R=332/3
R=110.67 TOTAL SPEED OF THE 2 CARS.
X+X+36=110.67
2X=110.67-36
2X=74.67
X=74.67/2
X=37.335 MPH FOR THE SLOWER CAR.
37.335+36=73.335 MPH FOR THE FASTER CAR.
PROOF:
332=(37.335+73.335)*3
332=110.67*3
332=332

You can put this solution on YOUR website!
I like to think of one train as standing still
and the other one approaching at the sum of their speeds
from 11 AM to 1 PM is 2 hrs
Let = the speed of the slower train
= the speed of the faster train
-----------------

The trains were traveling at 65 mi/hr and 101 mi/hr
check:

OK

Question 749531: Alex had a 4 mile head start on Mika. How long will it take Mika to catch Alex if Alex traveled at 6 miles per hour and Mika traveled at 8 miles per hour?
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Alex had a 4 mile head start on Mika. How long will it take Mika to catch Alex if Alex traveled at 6 miles per hour and Mika traveled at 8 miles per hour?
-----------------
Mika gains on Alex at 2 mi/hr (8 - 6)
4/2 = 2 hours

Question 749157: a map of the United States has a scale of 1 in.: 250 mi. The cities of Los Angeles, California, and Dallas, Texas are 5 3/4 inches apart on the map. Find the actual distance between these two cities.

You can put this solution on YOUR website!
Since 1in = 250mi set up a ratio:
250mi/1in * 5 3/4 in = ?
250*5.75 = 1437.5
ANS = 1437.5 miles

Question 748632: word problem: In order to pass a test with 80% with 70 questions. What is the highest number of questions I can answer incorrectly?
You can put this solution on YOUR website!
80% of 70, assuming all the questions are weighted the same, is 56. (.80)(70)=56
Thus, the minimum amount you could get right is 56 out of 70 for an 80%.
70-56=14
Therefore, you can miss 14 questions at most.
Alternatively, if you want 80% right, you could have at most 20% wrong.
20% of 70 is (.20)(70)=14

Question 748634: word problem:
There are 240 children in 5th grade, 1/3 are girls, what is the number of boys at school?

You can put this solution on YOUR website!
This question is essentially asking for 2/3 of 240 (why?)
2/3 of 240 is 2(240/3)=2(80)=160
There are 160 boys

:)

Question 747824: Hi, I can't understand the answer as explained in the link below.
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.477023.html

Can you kindly help me?
Thanks,
Moazzam

Question 747680: Two inches of heavy, wet snow are equivalent to 1 inch of rain. Estimate the water content in 3 inches of heavy, wet snow.
You can put this solution on YOUR website!
2 inches of snow = 1 inch of rain
therefore 1 inch of snow = 1/2 inch of rain
then 3 inches of snow = 3/2 inches of rain
or 1 1/2 inches of rain

Question 746486: isabel ran 9 miles with her friend kaylee last week. this was 60% of the distance she ran all week. how far did she run last week?
You can put this solution on YOUR website!
If 60% was equal to 9 miles
then 9/60 x 100 = 15 miles
This was the distance she
ran last week.

Question 746235: please help me solve this question ; aliff bought some lollipops and gave half of them to bob. bob bought some chocolates and gave half of them to aliff. aliff ate 4 chocolates and bob ate 7 lollipops. after that the number of chocolates and lollipops, aliff had were in the the ratio 1:8.the number of chocolates and lollipops bob had were in the ratio 1:5. how many lollipops did aliff give to bob?
You can put this solution on YOUR website!

please help me solve this question ; aliff bought some lollipops and gave half of them to bob. bob bought some chocolates and gave half of them to aliff. aliff ate 4 chocolates and bob ate 7 lollipops. after that the number of chocolates and lollipops, aliff had were in the the ratio 1:8.the number of chocolates and lollipops bob had were in the ratio 1:5. how many lollipops did aliff give to bob?

Aliff gave lollipops to Bob

You can do the check!!

Question 745736: what everyday object is 6 feet long?

You can put this solution on YOUR website!
Ans: a dining room table
-------
Cheers,
Stan H.

Question 745543: 1, 16, 4, 4 Write a proportion using the following numbers.
You can put this solution on YOUR website!
A ratio is a fraction x/y. A proportion is ratios that are equal x/y = w/z.

4/16 = 1/4

Question 745379: how much water (0% strength) should be added to 8L of 6% saline solution to reduce the strength to 4%?
How do I solve problems like this one?

You can put this solution on YOUR website!
how much water (0% strength) should be added to 8L of 6% saline solution to reduce the strength to 4%?
Equation:
salt + salt = salt
0.06*8 + 0*x = 0.04(8+x)
--------
6*8 + 0 = 4*8 + 4x
-----
2*8 = 4x
x = 4 L (amt. of water to add)
====================================
Cheers,
Stan H.
================

The smallest mammal, Kitti's hog-nosed bat has a head-body length of 1 7/50inches and a wingspan of about 5 1/10 inches. A scale drawing of this little bat is made showing it in full flight. The wingspan on the drawing is 15 inches. What should the length of the bat be in the drawing?
L= 1 7/50
15= 5 1/10
15 x 1.14 = 17.10 / 5.10 = 3.35 or 3 1/3
is this correct

You can put this solution on YOUR website!
The smallest mammal, Kitti's hog-nosed bat has a head-body length of
1 7/50inches and a wingspan of about 5 1/10 inches.
--------------------------
A scale drawing of this little bat is made showing it in full flight. The wingspan on the drawing is 15 inches. What should the length of the bat be in the drawing?
---
Use a proportion:
length/length = wing/wing
x/(57/50) = 15/(51/10)
----
x = (57/50)(150/51)
x = (57/1)(3/51)
x = (57/17) = 3.352 inches (length in drawing)

L= 1 7/50
15= 5 1/10
15 x 1.14 = 17.10 / 5.10 = 3.35 or 3 1/3
is this correct
-----
=======
Cheers,
Stan H.
==============

Question 745066: The sears Tower is 1450 feet tall. Jeff wanted to make a scale model for his class project, but his mother's car can hold only a 36 in tall model. What scale does Jeff need?
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The sears Tower is 1450 feet tall. Jeff wanted to make a scale model for his class project, but his mother's car can hold only a 36 in tall model. What scale does Jeff need?
-------------
36:1450
=~ 1:40.2777...
====================
He should make it 1:40 and find a different car to transport it.
It would be 36.25" tall

Question 744773: You have 100 random selected students . What is the probability half of the group has blue eyes ? What's the probability at least 25 percent of the group has blue eyes ?draw probability distribution for this exercise .
You can put this solution on YOUR website!
the probability that a random individual has blue eyes is 0.35.
-------------
You have 100 random selected students . What is the probability half of the group has blue eyes ?
----
z(0.5) = (0.5-0.35)/sqrt(0.35*0.65/100) = 3.1450
P(x > = 0.5) = P(z > 3.1450) = normalcdf(3.1450,100) = 0.0008309
---------------------------------------
What's the probability at least 25 percent of the group has blue eyes?
z(0.25) = (0.25-0.35)/sqrt(0.35*0.65/100) = -2.0966 = P(z > -2.0966)
= normalcdf(-2.0966,100) = 0.9820
=====================================

Draw probability distribution for this exercise .
Draw a normal curve with mean = 0.35 and std = sqrt[0.35*0.65/100) = 0.0477
============================
How many more people need to have blue eyes to be considered an outlier ??
If you take z >=2 as outlier region, determine the probability of the
distribution that is >= 2.
normalcdf(2,100) = 0.023
-----
Then the total # of the 200 with blue eyes would have to be
be >= 200(1-0.023) = 196,
Cheers,
Stan H.
----------------------------
==============

Question 744378: how to i solve
5/8 x = -40

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x=-40/(5/8)
x=-40*(8/5)
x=-64

Question 744316: on a map, 1 inch equals 25 miles. If two cities are 7 inches apart on the map, how far are they actually apart?
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If 1 inch = 25 miles then 7 inches = 7 x 25 = 175 miles

Question 744103: What Is n/5=27/45 what does n equal
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45n=135
n=135/45
n=3

Question 743536: w varies jointly as x and y and inversely as z. one set of values is w=112 x=4, y=8 and z= 0.2. Find w when x=8, y=10 and z=4
Answer by Edwin McCravy(8908)   (Show Source):
You can put this solution on YOUR website!

w varies jointly as x and y and inversely as z. one set of values is w=112 x=4, y=8 and z= 0.2. Find w when x=8, y=10 and z=4
For all proportion problems, start with this:

Varying           "directly" or product of "jointlys" or 1 if none
quantity  = k · ----------------------------------------------------------
inversely variable or product of "inverselys" or 1 if none

In this problem the varying quantity is w.
the "jointlys" are x and y.  We have one inversely,z.  So we have x·y
on top and z on the bottom:

w = k·

>>...one set of values is w=112 x=4, y=8 and z= 0.2...<<

Substitute these values:

112 = k·

112 = k·

112 = k·

Divide both sides by 112

= k

Now substitute  for k in the first equation:

w = k·

w = ·

w =

>>...Find w when x=8, y=10 and z=4...<<

Substitute those values

w =

w =

w = 14

Edwin

Question 743133: Three numbers are in the ratio 2:3:4. What are the numbers if their sum is 72?

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2N+3N+4N=9N
9N=72
N=72/9
N=8 ANS. FOR THE MULTIPLIER.
2*8=16 ANS. FOR THE SMALLER NUMBER.
3*8=24 ANS. FOR THE SECOND NUMBER.
4*8=32 ANS. FOR THE LARGER NUMBER.
PROOF:
16+24+32=72
72=72
2/16=3/24=4/32
1/8=1/8=1/8

Question 743081: sin:cos::1:3 find sin and cos
You can put this solution on YOUR website!
As if and . Imagine the triangle, hypotenuse of 1. , so

x=
from which you can find y.

Question 742432: What is the missing number in the proportion 4 : n = 3 : 9
You can put this solution on YOUR website!
4 : n = 3 : 9

4/n = 3/9

4*9 = 3n

36 = 3n

36/3 = n

12 = n

n = 12

If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples?

Found 2 solutions by MathLover1, richwmiller:
You can put this solution on YOUR website!

the total cost of apples is cents
let total number of apples is
cost of apple is
therefore cost of apples will be cents

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y*b/x=cost of y apples
each apples costs b/x

Question 741256: I have made 60 cupcakes. 36 are chocolate and 24 are vanilla. How many more chocolate do I need to make to have 70% of the cupcakes be chocolate. Please show the proportion used.

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I have made 60 cupcakes. 36 are chocolate and 24 are vanilla. How many more chocolate do I need to make to have 70% of the cupcakes be chocolate. Please show the proportion used.
-----
Proportion:
(# of chocolate)/(total # of cupcakes) = 70/100
-------
(36+x)/(60+x) = 70/100
----
36*100 + 100x = 70*60 + 70x
-----
30x = 600
x = 20 (# of chocolate to add)
============
Cheers,
Stan H.

Question 740792: I am rated at work either 4, 2, or 3 in 4 categories. Each category holds a weigh:
One is 40%; two are 25%; and one is 10%
In the 40% category I was rated 3 out of 4
In both 25% categories I was rated 3 out of 4
In the 10% category I was rated 2 out of 4
What should my total rating be? Can you please show me the calculation?
Thanks!

Question 740500: Set up a proportion for the following situation.It takes Todd 8 minutes to eat 5 pies at a pie eating contest. How many pies can Todd eat in 15 minutes?
You can put this solution on YOUR website!
Set up a proportion for the following situation.It takes Todd 8 minutes to eat 5 pies at a pie eating contest. How many pies can Todd eat in 15 minutes?
---
pies/min = pies/min
---
x/15 = 5/8
----
x = 15(5/8)
---
x = 75/8
----
x = 9.375 pies
===================
Cheers,
Stan H.
===================

Question 739971: I have tried to solve the following GMAT math problem for hours!
After spending 5/12 of his salary, a man has 140.00 dollars left. What is his salary?
The choices given were : 200.00. 240.00. 300.00. 420.00 583.00
The answer is. 240.00 I just do not understand how they got their answer.
The answer is based on the following: the man did not spend 7/12 of his salary. Ok, I got that understanding. However, they say that 140.00 represents 7/12 of his salary(I have no idea why they say this?) Set up a proportion where S is equal to his salary:
7/12 is equal to 140 divided by S. The answer is 240.00.
I tried to figure out the value of 1/12 . Forget that.
Then I set up the following proportion: If 5/12 is equal to 140, then 7/12 is equal to what value.
The answer I got was 336.00. That was not one of the choices.
I am completely stumped. Kindly help me with this supposedly easy proportion problem.
Sincerely, Ellen Motoi

You can put this solution on YOUR website!
Spent 5/12 of salary, still has 7/12 of salary which is 140 dollars.
, where S is the salary.

dollars.

Question 737320: A kilometer is about 5/8 mile. About how many miles are in 4 2/5? What is the proportion and what is the correct answer?
You can put this solution on YOUR website!
A kilometer is about 5/8 mile.
4 2/5=(4*5+2)/5=22/5
no of miles=(22/5)*(5/8)=11/4

Question 737098: How do I set these up?
It takes 13 people to pick 112 watermelons in a day. How many people would it take to pick 200 watermelons in a day?
Set up a proportion for the following situation.It takes Todd 8 minutes to eat 5 pies at a pie eating contest. How many pies can Todd eat in 15 minutes?

You can put this solution on YOUR website!
Watermelon example:
Use rate as watermelons per day and find the rate for 1 person.

If 13 people pick 112 watermelons in 1 day,
Then 1 person picks 112 watermelons in days. That is 112 melons per 13 days.

When people work together, their rates are added through simple arithmetic addition. For n count of people to pick watermelons, the rate will be melons per day.

What is wanted? What is n so that in t=1, the number of watermelons picked is 200. r*t=Q, where Q is count of melons picked, t is days of picking, and r is rate of the workers picking those melons.
In this situation, , and you want to find n, the number of workers who will pick those 200 melons in that one day.

Question 736619: A simple random sample of 250 Americans revealed that 112 of them owned a DVD player.
DVD companies, as an industry, brag that half of all Americans own a DVD player
At the 10% level, the DVD industry's claim should be
Rejected or not Rejected ?

Question 736578: if the actual distance between two cities is 157.5 miles and the distance on the map is 1 and 3/4 inches, what is the scale of the map?
You can put this solution on YOUR website!
157.5/1.75=90 miles:1 inch

Question 736539: I am having difficulty with this problem:
A gift of $6000 grew into$6,000,000 in 200 years. What is the interest rate if it is compounded annually?

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A gift of $6000 grew into$6,000,000 in 200 years. What is the interest rate if it is compounded annually?
--------
A(t) = P(1+(r/n))^(nt)
------
6 million = 6 thousand * (1+r)^(200)
-------
1000 = (1+r)^200
----
200*log(1+r) = log(1000)
------
log(1+r) = 3/200
-----
1+r = 10^(3/200)
1+r = 1.035..
rate = 0.035 = 3.5%
==========================
Cheers,
Stan H.
==========================

Question 736387: Hi,
Here is the problem I need help with-
The diameter of a dinner plate is 1 ft. In a dollhouse set, the
diameter of a dinner plate is 1 and 1/4 in.What is the ratio of the diameter of the
dollhouse plate to the diameter of the full-size plate?
This is what I have so far-
1ft= 12 in
I think I have to write as followed
1.25/12 in
but I don't know what to do?
Thank you

You can put this solution on YOUR website!
You have done great so far! Writing out the ratios in the correct order is a good place to start, now all we have to do is manipulate the numbers to give us whole numbers!
Ok! let's write the ratio as a fraction rather than a decimal, as that usually makes it easier to see what we have to do.
So we have
(That's one and a quarter to 12!)
Now we multiply BOTH NUMBERS in the ratio by the bottom of the fraction (this eliminates the fraction and turns it into a whole number)
Giving

multiplying out gives
5:48 (see how the fraction has gone!)
Since these numbers now have no common factors we cannot simplify this any further.
so the ratio of the dinner plates is
5:48

Question 736067: 190% of what number is 95?
You can put this solution on YOUR website!

Solve for

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 735855: James Caleb and Abigail bought a pizza. James ate 1//6 of the pizza and Caleb ate 1/4 of the pizza.
What fraction of the pizza did james and Caleb eat together? I got 5/12
Abigail ate 2/5 of the pizza that was remaining. What fraction of the original whole pizza did Abigail eat?

You can put this solution on YOUR website!
James Caleb and Abigail bought a pizza. James ate 1//6 of the pizza and Caleb ate 1/4 of the pizza.
What fraction of the pizza did james and Caleb eat together? I got 5/12
Correct
So there was 7/12 remaining.
-----
Abigail ate 2/5 of the pizza that was remaining.
-----------------------------------------
What fraction of the original whole pizza did Abigail eat?
She ate (2/5)(7/12 of the original)= 7/30 of the original area
===============
Cheers,
Stan H.
===============

Question 735681: JOSE RUNS 20 FEET IN 3 SECONDS HOW LONG DOES IT TAKE HIM TO RUN 100 FEET
You can put this solution on YOUR website!

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 735665: 2/7Y+3/8 =1/7Y+5/3
You can put this solution on YOUR website!
2/7Y+3/8 =1/7Y+5/3
2Y/7-Y/7=5/3-3/8
Y/7=(5*8-3*3)/(3*8)
Y/7=(40-9)/24
Y/7=31/24
24Y=7*31
24Y=217
Y=217/24
Y=9 1/24 ANS.

Question 735606: I have an unlimited number of bags containing marbles.
Each bag contains only two colors - black and one other color.
Some have 45% aquamarine marbles.
Some have 45% blue marbles
Some have 60% cyan marbles
If I take one bag of each color and mix all three bags together in a larger bag (in a ratio of 1:1:1) then the resultant bag would contain the following of each color represented as a percentage:
15% aquamarine marbles
15% blue marbles
20% cyan marbles
(based on the relationship that the final bag contains the 300 marbles so the percentages of each is calculated as total color marble/300).
If I enter a ratio of 2:1:2 then my final percentages are:-
18% aqua marbles
9% blue marbles
24% cyan marbles
What ratio of my original bags would I need to combine together to have a new bag containing a final percentage of the color marbles equaling:-
10% aquamarine marbles
5% blue marbles
20% cyan marbles
(I can use part of an original bag but must use the original percentage of black and color marbles e.g. I could use half of a blue bag which would yield 27.5 black marbles and 22.5 blue marbles)

You can put this solution on YOUR website!
1 QUESTION AT A TIME ONLY

Question 734167: 2 6
_______ = _______
x-1 2x+1