Questions on Word Problems: Problems on percentages, ratios, and fractions answered by real tutors!

Tutors Answer Your Questions about Percentage-and-ratio-word-problems (FREE)

Question 751091: The perimeter of a rectangle is 220 inches. The ratio of its length to its width is 7:3. Find the area of the rectangle.
Answer by stanbon(57327)

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The perimeter of a rectangle is 220 inches. The ratio of its length to its width is 7:3. Find the area of the rectangle.
-----
Equations:
Using Perimeter:
2(L+W) = 220
L+W = 110
L = 110-W
-------
Using ratio:
3L = 7W
L = (7/3)W
------
Solve:
Substitute to get:
110-W = (7/3)W
(10/3)W = 110
W = 3*11
W = 11
---
Solve for "L":
L = 110-W
L = 99
----
Find the Area:
Area = L*W = 99*11 = 1089 sq. units
===================================
Cheers,
Stan H.

Question 751079: If 480 students would eat the food in 16 weeks,but after two weeks, 80 students join, how long will it take them to finish the remaining food?
Answer by ankor@dixie-net.com(15649)

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If 480 students would eat the food in 16 weeks,
Find the number of "food-days" available
480*16*7 = 53760 food days
:
but after two weeks, 80 students join, how long will it take them to finish the remaining food?
Find number of food-days remaining after two weeks
53760 - (480*14) = 47040
Find how many days this will last with the additional students:
47040%2F%28480%2B80%29

= 84 days of food which is 84/7 = 12 weeks
:

Question 750990: A customer can choose one of six amplifiers, one of four compact disc players, and one of eight speaker models for an entertainment system. What is the number of possible system configurations? In other words, how many ways is possible?
Answer by JoeTaxpayer(112)

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6*4*8=192 possible systems

Question 750871: at a run fest awful 5/12 of the runners are women. if there are 144o runners how many are women?
Answer by Cromlix(322)

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5/12 of 1440 = 600 women

Question 750616: the rATIO of number of boy and girl in a school of 720 is 7:5. how many more girl should be admitted to make the ratio as 1:1

Answer by Cromlix(322)

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7 + 5 = 12
7/12 x 720 = 420 (boys)
Therefore there are 300 girls.
If 120 more girls were admitted
the ratio would be 1:1
420:420

Question 750727: 2 x reds, 2 x blues and 1 x green. The spinner is spun 30 times. How many reds, blues and greens would you expect?
Answer by timvanswearingen(104)

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For red, 2/5 of the spaces are red, so:
%282%2F5%29%2A30

This will be the same calculation for blue since 2/5 of the spaces are blue.
For green:
%281%2F5%29%2A30

Question 750731: is the ratio white 2 to 8 and there are a total of 30 pens, how many of them are white
Answer by Cromlix(322)

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The ratio is 2 : 8 Therefore 2 + 8 = 10
So 2/10 of 30 pens are white
= 6
And 8/10 of 30 pens are a different colour
= 24
Hope this helps.
:-)

Question 750530: Will you explain it too?
Madeline bought 11 feet of ribbon for $1.32 per yard. How much did she pay for the ribbon?
I know 3 ft = 1 yard
so 3 2/3 yards.
How do I change that to decimal to make money to multiple 1.32
1.32
x 3
-----
3.96
What do I do with the 2/3?
Answer by stanbon(57327)

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Madeline bought 11 feet of ribbon for $1.32 per yard. How much did she pay for the ribbon?
-------
11 feet = 11/3 yards
----
Value = (11/3)(1.32) = $4.84
==============================
Cheers,
Stan H.
===========

Question 750386: priscilla drinks on average of 3/4 quarts of water for each mile she walks.how many quarts of water will she drink if she walks 2/3miles?
i set it up like a proportion and cross multiplied but i got a answer of 6/6.can u pleas help me i would be very greatful thank you.
Answer by ankor@dixie-net.com(15649)

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priscilla drinks on average of 3/4 quarts of water for each mile she walks.
how many quarts of water will she drink if she walks 2/3 miles?
;
3%2F4

reduces to 1%2F2

qt of water

Question 750170: There are 18 girls in a class. Quarter of the class is boys. How many students arethere altogeather

Answer by Alan3354(30993)

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There are 18 girls in a class. Quarter of the class is boys. How many students arethere altogeather
--------------
1/4 boys --> 3/4 girls (assuming no dogs or cats or others)
s = total # of humans
18s = 3/4
6s = 1/4
s = 24

Question 750038: one-fourth percent of 18 is

Found 2 solutions by MathTherapy, lenny460:
Answer by MathTherapy(1423)   (Show Source):
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one-fourth percent of 18 is:

Answer by lenny460(766)   (Show Source):
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one-fourth percent of 18 is:
One-fourth is 25%
Therefore:
25/100 * 18 = 9/2
= 4.5

Answer:
4.5

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 748940: The cost of nursing home care in the United States will jump nearly 12% to $66 billion next year. Find the cost of nursing home care this year. Round to te nearest tenth of a billion.
Answer by richwmiller(9135)   (Show Source):
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1.12x=66
x = 58.9286
x=58.9 billion

Question 749089: a school has a total of 950 pupils. 400 pupils are boys and the rest are girls. what is the ratio of the number of boys to the number of girls

Answer by richwmiller(9135)   (Show Source):
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400/550=40/55=8/11

Question 750079: A jacket that normally costs $80 is marked down to $60.80. By what percent has the price been decreased?
19.20 X Cross multiply 19.20 * 100
_____ = _____ Cross multiply 80.00 * X
80.00 100
X= 24%
Answer by richwmiller(9135)   (Show Source):
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(1-( 60.80/80))*100=24%

Question 750102: If I have a 85% in my class (all assignment has been graded except final exam) and I received 51% in my final exam. The final is worth 30% of my grade. What is my grade now?
Answer by JoeTaxpayer(112)   (Show Source):
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(.7 * .85) + (.3 * .51)
.595 + .153 = .748
this should round to 75% and looks likes a passing grade.

Question 750062: I have saved 140 hours of movies on my DVR. The DVR says I have used 40% of available space. How do I calculate what is 100% is, or how many hours total space I have?
Answer by Cromlix(322)   (Show Source):
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If you have 140 hours of movies on
your DVR and this equates to 40%
then 100% will equal (140/40) x 100
= 350 hours.
Happy viewing.
:-)

Question 749504:
At the gym club there is 2 boys for every 3 girls there is 50 children how many girls are there?
Answer by checkley79(3050)   (Show Source):
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2M+3M=50
5M=50
M=50/5
M=10 THIS IS THE MULTIPLIER FOR THE RATIOS.
2*10=20 BOYS.
3*10=30 GIRLS
PROOF"
20+30=50
50=50

Question 749472: There are 30 buttons in a box
12 of the buttons are black
The rest of the buttons are white.
What is the ratio of the number of black buttons to the number of white buttons?
Answer by lynnlo(4155)   (Show Source):
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12:18

Question 749438:
a total of R9000 was invested in two funds. one fund pays 5% interest and the other funs pays 6% interest annually. the combined annual interest is R510. work out how much of the money was invested in each fund
Answer by checkley79(3050)   (Show Source):
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.06x+.05(9000-x)=510
.06x+450-.05x=510
.01x=510-450
.01x=60
x=60/.01
x=$6,000 invested @ 6%.
9,000-6,000=$3,000 invested @ 5%.
Proof:
.06*6,000+.05*3,000=510
360+150=510
510=510

Question 749341: Can You Please Help Me With This Question, "The retail price of a leather jacket is $90.00, but this weekend it is 20 percent off. How much will it cost?"
Answer by tommyt3rd(528)   (Show Source):
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we take 20% of 90, which is (90)(20/100)=18
therefore we pay 90-18=72
72 dollars

:)

Question 748952: The average selling home price in the united states last year was $202,250 while the average selling price this year was $215,400. What is the perecent of increase? Round to the nearest tenth of a percent.
Answer by Cromlix(322)   (Show Source):
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$215,400 - $202,250 =$13,150
($13150/$202,250) x 100
= 6.5%

Question 748954: At a recent health fair 32% of the people tesred were found to have high blood cholesterol levels. If 350 people were texted, find the number haveing high blood cholesterol.
Answer by stanbon(57327)   (Show Source):
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At a recent health fair 32% of the people tesred were found to have high blood cholesterol levels. If 350 people were texted, find the number haveing high blood cholesterol.
---
Use a Proportion:
x/350 = 32/100
----
x = 350(32/100)
----
x = 112
==============
Cheers,
Stan H.
===========

Question 748399: How many liters of a 75% saline solution must be mixed with 8 liters or pure water to make a 35% saline solution.
Answer by josgarithmetic(1507)   (Show Source):
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Not sodium chloride in water. It could not be more than about 25%. Not sodium chloride in some other solvent; it is more soluble in water than other solvents.

Ignoring that but just going into the arithmetic,

liters of ....

Question 748142: 2.5% OF 1 HOUR 40 MINUTES
Answer by stanbon(57327)   (Show Source):
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2.5% OF 1 HOUR 40 MINUTES
----
1 hr 40 min = 100 minutes
-----
2.5%*100 = 2.5 minutes
=============================
Cheers,
Stan H.

Question 747763: In 5 minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 8 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
Answer by stanbon(57327)   (Show Source):
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In 5 minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 8 minutes. If both belts are used, find how long it takes to move the cans to the storage
---------------
Larger belt DATA:
time = 5 min/job ; rate = 1/5 job/min
------------
Smaller belt DATA:
time = 8 min/job ; rate = 1/8 job/min
-----
Together DATA:
time = x min/job ; rate = 1/x job/min
---------------
Equation:
rate + rate = together rate
1/5 + 1/8 = 1/x
8x + 5x = 40
13x = 40
x = 3.08 minutes = 3 min 4.8 seconds
-------------
Cheers,
Stan H.

Question 746988: The value of a professional basketball player's autograph rose 20% in the last year. It is now worth $252.00. What was it worth a year ago?
Answer by Cromlix(322)   (Show Source):
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$252 x 100/80
= $315

Question 747713: If a recipe requires 3 cups of milk for 2 cups of flour, how many cups of flour is needed if
your will use 8 cups of milk? Round to the nearest tenth of a cup if needed.
Answer by Cromlix(322)   (Show Source):
You can put this solution on YOUR website!
If the recipe requires 3 cups milk
for 2 cups of flour, then 1 cup of milk
requires 2/3 of a cup of flour.
Then 8 cups of milk require 2/3 x 8
cups of flour or 5.3 cups of milk.

Question 747736: in a certain class if there are 35 men and 63 women then the ration b/w them is
Answer by Cromlix(322)   (Show Source):
You can put this solution on YOUR website!
Divide both ratios by a common number till you
can't divide any further down.
35:63 Divide by 7
5:9 This is as far down as it will go.

Question 747465: if there are 18 girls in a class, and a quarter of the class are boys, how many children are there in the class in total
Answer by Cromlix(322)   (Show Source):
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If a quarter of the class are boys
then three quarters are girls
Therefore if 3/4 = 18
1/4 = 6
There are 24 children in the class in total

Question 747432: Today oil is $90.00 a barrel, which is 175% of the cost in 2000. What did oil cost a barrel in 2000?
Answer by mikeebsc(26)   (Show Source):
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I'm guessing your problem lies in calculating percentages and/or word problems. These are very easy and I will try and explain. A percent is simply a number * 100 (or a number moved 2 decimal places to the right). Knowing this, if you need to, write 175% as 175.00%, and convert it back to a "regular" number. If we got the % by moving the decimal 2 places to the right, to get it back to a regular number, we simply move it 2 places to the left. So
175.00% = 1.75
Let's work on translating English to math.
Now that we have 2 whole numbers the problem reads "Today oil is 90.00 a barrel, which is 1.75 of the cost in 2000".
Now we let x represent an unknown value (the cost in 2000) we are trying to solve for. If need be you can write the problem again as "Oil is 90 a barrel = 1.75 of x" (notice we replaced the entire phrase "the cost in 2000" with x). The word "of" means we multiply, so we can write "Oil is 90 a barrel = 1.75x". We can leave out any words that don't really matter to the math part of the problem such as "oil is and "a barrel" if you feel comfortable doing so. Leave out any steps you feel comfortable with, as what I am showing you is the most detailed you can get. I am just trying to show you how to literally translate the language of English to the language of math, and we end up with:
90=1.75x
Swap it around so the x is on the left:
1.75x=90
Divide both sides by 1.75 to cancel out the 1.75 in front of the x, or:
1.75x/1.75=90.00/1.75 which leaves us x=90.00/1.75
Now we solve for x. Do the simple math of 90/1.75 and
x=51.4285 and round to the nearest hundredth (since this is how we represent dollars)
x=51.43
If your teacher requires you to, don't forget to write this as a dollar value, since that is what the problem was looking for ($51.43).
Hope this helps you. After doing this a while, you will just be able to look at the problem and know to divide 90 by 1.75, but when just starting, show your work so your teacher can show you where you made a mistake, if you make one (everybody does...trust me). I've gotten many more wrong than I have right:)
Good Luck!

Question 747429: The ratio of men to women in elementary education courses is 2 to 7. If there are 270 students in an elementary education course, how many are women? What percent of the elementary education students are men?
Found 2 solutions by lenny460, JoeTaxpayer:
Answer by lenny460(766)   (Show Source):
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The ratio of men to women in elementary education courses is 2 to 7. If there are 270 students in an elementary education course, how many are women ? What percent of the elementary education students are men ?

7/9 * 270 = 7 * 30 = 210

Answer:
There are 210 women.

Percentage of men:
There are 60 men.
Therefore:
60/270 * 100 = 20/9 * 10 = 200/9 = 22.2%

Answer:
22.2%

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Answer by JoeTaxpayer(112)   (Show Source):
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The ratio simply means that 2 of every nine are men. So 7 of 9 are women.
7/9 * 270 = 210 women.
2/9 = .22... (2 repeats)

Question 747312: WHAT IS 1/3 OF 480?

Answer by lenny460(766)   (Show Source):
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WHAT IS 1/3 OF 480 ?

1/3 of 480 = 160

Answer:
160

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 747307: Jim bought a basketball for $12. The Basketball was market 25% off. What is the original price?
***How do you write that as an equation?
Answer by JoeTaxpayer(112)   (Show Source):
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X - .25X = 12
.75 X = 12
X = 12/.75
X = 16

Question 747315: WHAT IS 1/4 OF 480?

Answer by tommyt3rd(528)   (Show Source):
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1/4 of 480 can be found by dividing 480 by 4, so it is 120

:)

Question 747090: you can buy 4 pieces of candy for a quarter. how much will one piece cost

Answer by lenny460(766)   (Show Source):
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You can buy 4 pieces of candy for a quarter. How much will one piece cost ?
One quarter = 25 cents
Therefore:
25 / 4 = 6.25

Answer:
6.25 cents

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 747051: an automobile tank is 1/6 full of gasoline. when eight litres are added to the tank, it is 1/4 full of gasoline. how many litres of gasoline does the tank hold
Found 2 solutions by lwsshak3, stanbon:
Answer by lwsshak3(6494)   (Show Source):
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an automobile tank is 1/6 full of gasoline. when eight litres are added to the tank, it is 1/4 full of gasoline. how many litres of gasoline does the tank hold.
***
let x= litres of gasoline the tank holds.
x/6+8=x/4 (1/6 capacity+8 litres=1/4 capacity)
x/4-x/6=8
3x/12-2x/12=8
x/12=8
x=96 litres of gasoline the tank holds.

Answer by stanbon(57327)   (Show Source):
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an automobile tank is 1/6 full of gasoline. when eight litres are added to the tank, it is 1/4 full of gasoline. how many litres of gasoline does the tank hold
------
Let the tank capacity be "x" litres.
-----
Equation:
(1/6)x + 8 = (1/4)x
--------
Multiply thru by 12 to get:
2x + 96 = 3x
x = 96 litres
=====================
Cheers,
Stan H.

Question 746912: Subas packed 5 dozen Oranges in a box. If he put 1and 3 fourths dozen in each box , how many boxes did he pack
Answer by josgarithmetic(1507)   (Show Source):
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Five dozen is cut into equal portions of dozen each.
and the unit is .

COMPUTATION

This is , which needs to be 3 boxes.

ALTERNATIVE CHECK:
5 dozen is 60.
One and three quarters dozen is 21.
, not bad. Same as .

Question 746924: A family is given a sum of $93,600 to be shared among five children Ann,Betty,Carol,Donna,and Elsie in the ratio 2:4:6:8:10.Use the information above to:(a)calculate each child's share
Found 2 solutions by timvanswearingen, Cromlix:
Answer by timvanswearingen(104)   (Show Source):
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First off, add up the numbers from the ratio to see what portion of the total money each child receives.

Now, Ann will get 2/30 of the money. Betty will get 4/30, Carol will get 6/30, Donna will get 8/30 and Elsie will get 10/30.
For Ann,
(2/30)*($93,600)=$6,240
For Betty,
(4/30)*($93,600)=$12,480
For Carol,
(6/30)*($93,600)=$18,720
For Donna,
(8/30)*($93,600)=$24,960
For Elsie,
(10/30)*($93,600)=$31,200

Answer by Cromlix(322)   (Show Source):
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Totalise the ratios = 30

Ann 2/30 or 1/15 = $6240
Betty 4/30 or 2/15 = $12480
Carol 6/30 or 1/5 = $18720
Donna 8/30 or 4/15 = $24960
Elsie 10/30 or 1/3 = $31200

Question 746768: The price of a refrigerator is increased by 50%. It then goes on sale, with the new sale price equaling 75% of the original price. The sale price is what percent of the increased price?
I am a soldier overseas. Can you help with the above math problem?
Answer by Alan3354(30993)   (Show Source):
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The price of a refrigerator is increased by 50%. It then goes on sale, with the new sale price equaling 75% of the original price. The sale price is what percent of the increased price?
====================
P = original price
= 1.50P with the increase
- 0.75P new sale price
----------
= 0.75P = 75% of the original price

Question 746684: In science class,There are 25 students .44% of the students are boys.How many boys in science class?
Answer by Cromlix(322)   (Show Source):
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44/100 x 25 = 11 boys

Question 746751: one quarter of the pupils in jane's class are boys. find the fraction of the class who are girls if there are 60 pupils in the class. how many are boys

Answer by Cromlix(322)   (Show Source):
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If the one quarter of the class are boys,
then three quarters of the class are girls.
If there are 60 pupils in the class then
one quarter of 60 = 15 boys
1/4 x 60 = 15