Questions on Word Problems: Numbers, consecutive odd/even, digits answered by real tutors!

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Question 113504: The sum of two numbers is 22. Five times one number is equal to 6 times the second number. Find the numbers.
x + y = 22
5x = 6y
I believe these are the correct equations, but I am drawing blanks. I know the answer is x=12, y=10 just from the second equation, but I cannot do it algebraically.
Click here to see answer by ptaylor(2048)

Question 113430: The area of a rectangle of length x is given by 3x^2+5x. Find the width of the rectangle.
Click here to see answer by ptaylor(2048)

Question 113520: The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.

here is what I have done:

original number 10x + y
new number 10y + x
x + y = 7

10x + y = 10y + x + 3
10x -x + y -y = 10y -y + x -x + 3
9x = 9y + 3
x = y + 3

x + y = 7
(y+3) + y = 7
2y + 3 = 7
2y +3 -3 = 7 -3
2y = 4
2y/2 = 4/2
y = 2
x + y = 7
2 + y = 7
2 -2 + y = 7 -2
y = 5
x = 2
I get an answer, but it don't check.
Every time I do this problem this my answer or fractional. please help
Click here to see answer by kev82(148)

Question 113420: The retail selling price of a sofa is $806.25. What is the cost to the dealer if she sells at 25% markup on the cost?
Click here to see answer by scott8148(6628)

Question 113544: There are 7 girls on a bus
Each girl has 7 backpacks
In each backpack, there are 7 big cats
For every big cat there are 7 little cats
Question: How many legs are there in the bus?
I thought it might be
7*4*7=196 cats legs per bag
there are 7 bags so you have 196x7=1372+14=1386 legs per girl
so we take 1386x7=9702 legs on the bus.
Is this correct or did I not do the math properly?
Click here to see answer by stanbon(57323)

Question 113426: A=1/2(b+B) solve for B
Click here to see answer by Fombitz(13828)

Question 113567: During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday? 9315 is the answer I need to know the equation
Click here to see answer by stanbon(57323)

Question 113809: John can paint the house in 4 hours. Mike can paint the same house in 6 hours. How long would it take both John and mike to paint the same house together.
Click here to see answer by stanbon(57323)

Question 114139: Can you help me please to solve this equation:The sum of three consecutive integers is 78.Find the number.
Thanks

Click here to see answer by jayanthihemkos@yahoo.com(87)

Question 114246: What is the solution to the following question "find three consecutive integers whose sum is 303" i missed cass one day and now i am confused with the steps.

Click here to see answer by SHUgrad05(58)

Question 114217: I need some help....please!
The sum of two numbers is 40. The sum of twice the larger and 4 times the smaller is 108. Find the numbers.
Click here to see answer by bucky(2189)

Question 114335: if 3 students can fill 4 baskets in 12 minutes, how many baskets can 4 students fill in 18 minutes?
Click here to see answer by stanbon(57323)

Question 114448: Please Help.
Solve the following problem.
Number problem.
The sum of two numbers is 40. If their difference is 10, find the two numbers.
Please show the equation used.
Thanks
JMS

Click here to see answer by jim_thompson5910(28593)

Question 98168: What are the five odd numbers that their sum is equal to fifty?
Click here to see answer by jgr45(22)

Question 114504: The sum of two numbers is 39 and their difference is 7. What are the numbers?
Click here to see answer by ptaylor(2048)

Question 114630: The product of two consecutive natural numbers is 1056. Find the sum of these two numbers.
Click here to see answer by Earlsdon(6287)

Question 114865: A group of goats and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are goats. How many are there of each?
Click here to see answer by solver91311(16877)

Question 115230: When one half of the second of two consecutive integers is subtracted from the first of the two consecutive integers, the result is 2.
Click here to see answer by bucky(2189)

Question 115477: A two-digit number is five times its units digit. if the digits are reversed the resulting number is 27 more than the original number, find the original number?
Click here to see answer by ankor@dixie-net.com(15649)

Question 115650: find three consecutive odd integers such that the sum of the smallest and 4 times the largest is 61
Click here to see answer by MathLover1(6627)

Question 115760: tell whether this is always never or sometimes true
the sum of two consecutive even numbers equals the sum of two consecutive odd numbers
Click here to see answer by edjones(7569)

Question 115819: tell whether this is always sometimes or never true
the sum of two consecutive even numbers is equal two the sum of two consecutive odd numbers
Click here to see answer by ankor@dixie-net.com(15649)

Question 116140: . A solid metal cube of side 6 inches is placed in a rectangular tank whose length, width, and height are 1, 2, and 3 feet. What is the volume, in cubic units, of water that the tank can now hold?

Click here to see answer by bucky(2189)

Question 116231: two numbers differ by 6. if the numbers are squared and then added, the result is 146. what are the two numbers?
Click here to see answer by edjones(7569)

Question 116309: Good evening ma'am or sir. Would you please help me in solving this word problem:
1). The tens' digit of a two-digit number is on more than the units' digit. If the number is divided by the sum of the digits, the quotient is equal to seven. What is the number? Thank you ma'am or sir for your generosity.
Click here to see answer by stanbon(57323)

Question 116344: If c does not equal 0 and the slope of the line passing through (-c, 2c) and (4c, a) is 1, what is the expression for a in terms of c? Hint: Set up the slope formula, substitute, and solve the resulting proportion (cross multiplication).

Click here to see answer by ilana(307)

Question 116439: Find all sets of three consecutive multiples of 6 whose sum is between -6 and 50.
I did it as -
-6 < 3x + 18 > 50
= -8 < x > 10.4
What is the correct answer?

Click here to see answer by checkley71(8403)

Question 116596: By what percent does the volume of a cube increase when the length of each of its sides is tripled?
Isn't it 300%, my teacher said 2600% now how???

Click here to see answer by MathLover1(6627)

Question 116670:
The sum of two numbers is 42. one number is 3 less than 4 times the other number. what are the numbers?
i just need to know how to translate it to algebraic form and then everything else is fine.
Click here to see answer by checkley71(8403)

Question 116921: twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71.What are the numbers?
Click here to see answer by stanbon(57323)

Question 116943: Number problems. Find two consecutive positive integers such that the sum of their squares is 85.
Click here to see answer by ganesh(20)

Question 117440: A printer can print 1 page in 6 seconds. It shuts down for 2 minutes to cool off after every hour of operation. How many minutes will it take the printer to print 4500 pages?
Just checking is it 462?
600 pages in 1hr
4500 pages= 7.5 hours + ( 6hrs x 2 cooldown)=another 12 min = 462 min?
Click here to see answer by psbhowmick(529)

Question 117442: A jar contains 5 white, 7 blue, and 8 red marbles. If you remove 1 marble at a time, randomly, what is the minimum number that you must remove to be certain that you have at least 3 marbles of each color?
Click here to see answer by bucky(2189)

Question 117439: Your mother's friend Agnes was born on September 14, 1932 and died on March 23, 2004. How old was she? She wasn't 72 fyi
Click here to see answer by bucky(2189)

Question 117443: There are 100 people in line. Jack is the 28th person in line and Jill is the 68th person in line. If a person in line is chosen at random, what is the probability that the person is standing between Jack and Jill?
Click here to see answer by bucky(2189)

Question 117441: Let A be the set of all composites less than 10, and B be the set of positive even integers less than 10. How many different sums of the form a + b are possible if a is in A and b is in B?
Click here to see answer by Fombitz(13828)

Question 117395: one number is 11 more than another number. Find the two number if three times the larger exceeds four times th smaller number by 4.
this is from the textbook ISBN 9789710438013
Click here to see answer by ankor@dixie-net.com(15649)

Question 117552: write an equation and solve the following:A reception costs $235 plus $6 for each guest.The total bill is $1081. How many guests attended?
Click here to see answer by edjones(7569)

Question 117461: In a group of 150 students, more students are taking a math class than are taking a science class this semester. If 80 are taking a science class and 25 are not taking either math or science this semester, what is the minimum number of students who could be taking both math and science this semester?
Is it 81? I was trying to take an example from the book and I don't know if my equation is correct
Click here to see answer by ankor@dixie-net.com(15649)

Question 117720: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
Click here to see answer by stanbon(57323)

Question 117752: 2, 6 , 18 , 54 , ....
In the sequence above what would be the 8th term?
Click here to see answer by josmiceli(9671)

Question 117751: 2, 6 , 18 , 54 , ....
In the sequence above what would be the 8th term?
Click here to see answer by jim_thompson5910(28593)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845