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# Recent problems solved by 'chana'

 Geometry_Word_Problems/733622: half the perimeter of a rectangular lot, which is 50 feet longer than it is wide, is 350 feet. what are the dimensions of the lot?1 solutions Answer 448508 by chana(69)   on 2013-04-04 02:03:29 (Show Source): You can put this solution on YOUR website!Perimeter of the rectangle = 2L+2B L=B+50 half the perimeter of a rectangular lot, which is 50 feet longer than it is wide, is 350 feet So, .5*(2* (B+50))+(2B))= 350 4B+100=700 solving for B we get, B as 150 feet And L= 150+50 =200 feet
 Money_Word_Problems/733627: 1 )The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening company will charge \$195 set up fee and \$3.50 per T-shirt ordered. The PTA is charging \$5 per shirt to students. a. Write an equation for the total cost, C, of ordering t T-shirts. b. b. Write an equation for the revenue, R, for selling t T-shirts. c. Write an equation for the profit, P, made by the PTA for selling the shirts. d. (1 point) How many shirts does the PTA have to sell before they start making money for their fundraiser? e. (1 point) If the PTA needs to raise \$5000 for the new track field, how many T-shirts do they need to sell? 1 solutions Answer 448505 by chana(69)   on 2013-04-04 01:49:15 (Show Source): You can put this solution on YOUR website! 1)The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening company will charge \$195 set up fee and \$3.50 per T-shirt ordered. The PTA is charging \$5 per shirt to students. a. Write an equation for the total cost, C, of ordering t T-shirts. b. b. Write an equation for the revenue, R, for selling t T-shirts. c. Write an equation for the profit, P, made by the PTA for selling the shirts. d. (1 point) How many shirts does the PTA have to sell before they start making money for their fundraiser? e. (1 point) If the PTA needs to raise \$5000 for the new track field, how many T-shirts do they need to sell? Ans: Consider fixed cost(FC)= 195\$ Cost pice = 3.50\$ Selling price = 5\$ a.total cost = t*3.50 + 195 Where t= no of shirts ordered . total cost and fixed cost .The above question is answered on the basis that all the expense includes FC+Variable cost Where variable cost here is cost of one shirt *total ordered. b.Revenue= t*5\$ where t= toal shirts ordered. c.P = revenue - Total cost =(t*5)-(t*3.50 + 195) d.this is calculated by using break even point, in that point there will be no profit and no loss, after this poin, the company faces profit. break even quantity = FC/(CP-SP per unit) =195/(5-3.5) =130 shirts. So this company have to sell 130 shirts to make a profit. e.use this formula P = Total revenue - total cost 5000= (X*5)-(X*3.50 + 195) Where X is the total number of shirts to be sold to attain a profit of 5000\$ Solving for X we get 3203 (rounded for nearest whole number)i.e., number of shirts to be sold.
 Percentage-and-ratio-word-problems/733639: Have a total of 15 students with the following grades: A = 5 students, B = 4 students, and C = 6 student. How do I get pecentages of A's, B's, and C's that equal 100%1 solutions Answer 448501 by chana(69)   on 2013-04-04 01:27:17 (Show Source): You can put this solution on YOUR website!just express all the students of the particular grade as a fraction of the total students: A's %=(5/15)=.33 B's %=(4/15)=.27 C's %=(6/15) =.4 i.e., 33%, 27% , 40% respectively...
 Age_Word_Problems/733640: The sum of the ages of a father and his son is 56 years.Seven years ago the father was five times as old as his son.Find the age of the father now.1 solutions Answer 448497 by chana(69)   on 2013-04-04 01:17:45 (Show Source): You can put this solution on YOUR website!The sum of the ages of a father and his son is 56 years.Seven years ago the father was five times as old as his son.Find the age of the father now. Ans: take 7 years back, Son=X Dad= 5X Now,The age of the son = X+7 The age of the dad = 5X+7 As, sum of the ages of a father and his son is 56 years (X+7)+(5X+7)=56 6X+14=56 6X = 42 X=7 Dad age, 7*5=35 i.e., 7years back. So the age of the father now is 35+7= 42 years
 Equations/733636: I need some help on solving this equation: 7x-5x+15=x+81 solutions Answer 448495 by chana(69)   on 2013-04-04 01:00:34 (Show Source): You can put this solution on YOUR website!7x-5x+15=x+8 Bring X one side and constants to the other side.. So if you rearrange 7x-5x-x= 8-15 x= -7
 Money_Word_Problems/733632: if 30 cans equals 50 cent and 60 cans equals a dollar how many cans would take to reach\$50001 solutions Answer 448494 by chana(69)   on 2013-04-04 00:51:56 (Show Source): You can put this solution on YOUR website!60 cans takes 1\$---------------- 1 so X cans takes 5000\$------------ 2 Cross multiply the above two eqns 60*5000 = X cans so, total cans = 300,000
 Numbers_Word_Problems/621383: one number is 12 more than another.the larger is 7 times smaller.what are the numbers?1 solutions Answer 390746 by chana(69)   on 2012-06-17 11:51:27 (Show Source): You can put this solution on YOUR website!one number is 12 more than another.the larger is 7 times smaller.what are the numbers? ans: let one no be X and anothr no be y one number is 12 more than another : so X = Y +12----- (1) the larger is 7 times smaller : SO X = 7*Y ---- (2) SUBS 2 IN 1 , YO WILL GET THE ANSW....
 Permutations/576841: number of ways in which 6 men and 5 women can dine at a round table if no 2 women are to sit together is given by?1 solutions Answer 370019 by chana(69)   on 2012-02-23 09:19:16 (Show Source): You can put this solution on YOUR website!number of ways in which 6 men and 5 women can dine at a round table if no 2 women are to sit together is given by? sol : x is the position of the men y is the position of the women yxyxyxyxyxyxy in the above pattern with 6 man ,in 7 positions the 5 women can be placed so total ways = 7c5 = 42 ways
 Numbers_Word_Problems/576860: 1.IF THE SUM OF TEN CONSECUTIVE POSITIVE INTEGERS IS 115, FIND THE LARGEST OF THESE INTEGERS. 2.THREE CONSECUTIVE INTEGERS HAVE A SUM OF 12 AND A PRODUCT OF 60. IF THE SMALLEST INTEGER IS 3 FIND THE LARGEST NUMBER.1 solutions Answer 370018 by chana(69)   on 2012-02-23 09:11:11 (Show Source): You can put this solution on YOUR website!1.IF THE SUM OF TEN CONSECUTIVE POSITIVE INTEGERS IS 115, FIND THE LARGEST OF THESE INTEGERS. sol : let the nos be x , x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9 so 10x + 45 = 115 solve tis you will get x = 7 substitute in the 10th number = x + 9 largest no = 16 2.THREE CONSECUTIVE INTEGERS HAVE A SUM OF 12 AND A PRODUCT OF 60. IF THE SMALLEST INTEGER IS 3 FIND THE LARGEST NUMBER. sol : if first no is 3 so ,the third consecutive number is 3 + 2 = 5 , which is the largest.
 test/576869: the coat of 3 large candles and 5 small is 6.40. the cost of 4 large candles and 6 small candles is 7.50 which pair of equation can be used to determine, t, the cost of a large candle and s, the cost of a small candle.1 solutions Answer 370015 by chana(69)   on 2012-02-23 08:55:23 (Show Source): You can put this solution on YOUR website!the coat of 3 large candles and 5 small is 6.40. the cost of 4 large candles and 6 small candles is 7.50 which pair of equation can be used to determine, t, the cost of a large candle and s, the cost of a small candle. sol: let t,be the cost of a large candle and s,be the cost of a small candle. 3t + 5s = 6.40--------1 4t + 6s = 7.50--------2 the above two equations help in finding t & s
 Age_Word_Problems/576862: In 5 years, Alessandro will eb three times as old as Frederico will be then. The sum of their ages now is 86. How old will each of them be in 3 years?1 solutions Answer 370014 by chana(69)   on 2012-02-23 08:52:29 (Show Source): You can put this solution on YOUR website!In 5 years, Alessandro will eb three times as old as Frederico will be then. The sum of their ages now is 86. How old will each of them be in 3 years? sol: let ales age = x fred age = y in 5 years, (x+5) = 3(y+5)---------- 1 present; x + y = 86 ---------- 2 solve 1 & 2 as equations which gives x = 67 , y = 19 so after 3 years , x = 70 , y = 22
 Travel_Word_Problems/576856: Marcella traveled for 45 minutes at an average rate of 40 miles per hour. How far did Marcella travel?1 solutions Answer 370012 by chana(69)   on 2012-02-23 08:39:31 (Show Source): You can put this solution on YOUR website!Marcella traveled for 45 minutes at an average rate of 40 miles per hour. How far did Marcella travel? sol: distance = speed * time =40 * 3/4 (3/4 = 45/60 --- converting to hours) = 30 miles
 Mixture_Word_Problems/576777: How many gallons of hydrochloric acid must be added to 12 gallons of a 30% solution to obtain a 40% solution?1 solutions Answer 369998 by chana(69)   on 2012-02-23 02:17:04 (Show Source): You can put this solution on YOUR website!How many gallons of hydrochloric acid must be added to 12 gallons of a 30% solution to obtain a 40% solution? sol: x be the extra added solution 30% of 12 gallons = 3.6 gall. so forming the equation : ( 3.6 + x)/(12+x) = 40 / 100 solve for x you will get the required quantity which is 2 gallons
 Mixture_Word_Problems/576781: The bookstore sold 348 notebooks the first day of classes, some at \$2.85 each and the rest at \$3.95 each. The total amount taken in was \$1154.60. How many of each kind of notebook were sold?1 solutions Answer 369997 by chana(69)   on 2012-02-23 02:08:34 (Show Source): You can put this solution on YOUR website!The bookstore sold 348 notebooks the first day of classes, some at \$2.85 each and the rest at \$3.95 each. The total amount taken in was \$1154.60. How many of each kind of notebook were sold? sol: let x be one kind of note book 348 - x be the other kind of notebook as given : (2.85 * x) + ((348 - x) * 3.95) = 1154.60 here solve for x you will get x = 200 & the other kind notebook as 148
 Permutations/576795: Suppose a dice is tossed.What is the probabilitythat at most one 6 appears.1 solutions Answer 369995 by chana(69)   on 2012-02-23 02:02:48 (Show Source): You can put this solution on YOUR website!Suppose a dice is tossed.What is the probabilitythat at most one 6 appears. sol: here S = (1,2,3,4,5,6) E be the event of getting 6 P(E) = N(E)/N(S) = 1/6
 Permutations/576797: Five girls and five boys are getting together for a party.Suppose one of the boys has 2 sisters amoung the five girls, and he would not accept either of them as a partner.How many couples can be formed1 solutions Answer 369994 by chana(69)   on 2012-02-23 02:00:23 (Show Source): You can put this solution on YOUR website!Five girls and five boys are getting together for a party.Suppose one of the boys has 2 sisters amoung the five girls, and he would not accept either of them as a partner.How many couples can be formed sol : i gues this will be the solution do check the answer with your friends ... (1 from 5 boys) * (1 from 3 girls ) = total ways 5c1 * 3c1 = 15 ways
 Numbers_Word_Problems/576785: eight times the larger of two numbers decreased by three times the smaller is 148. nine times the smaller decreased by twenty is equal to eight times the larger. find the two numbers1 solutions Answer 369993 by chana(69)   on 2012-02-23 01:53:25 (Show Source): You can put this solution on YOUR website!eight times the larger of two numbers decreased by three times the smaller is 148. nine times the smaller decreased by twenty is equal to eight times the larger. find the two numbers sol : forming the equation with the given datas : let x be the larger number and y be the smaller number so as given 8x - 3y = 148 ------(1) 9y - 20 = 8x ----------(2) solve the anove two equation for x & y ,you will get the required nos ,where x = 29 , y = 28.
 Age_Word_Problems/576787: charels is twice as old as william.Four years ago Charles was 3 times as old as william.How old is each now?1 solutions Answer 369992 by chana(69)   on 2012-02-23 01:46:32 (Show Source): You can put this solution on YOUR website!charels is twice as old as william.Four years ago Charles was 3 times as old as william.How old is each now? sol: let william's age = x charle's age = 2x ,as given forming the equation with the data they gave, 2x - 4 = 3(x - 4) solve for x you will get william's = 8 years charle's = 16 years
 Travel_Word_Problems/576041: a train leaves Philadelphia for Atlanta at 12 noon, traveling 70 mph. another train leaves Atlanta for Philadelphia at 2pm traveling 60 mph. The distance from Philadelphia to Atlanta is 400 miles. Where d the trains meet? When do they meet? 1 solutions Answer 369780 by chana(69)   on 2012-02-22 10:29:45 (Show Source): You can put this solution on YOUR website!a train leaves Philadelphia for Atlanta at 12 noon, traveling 70 mph. another train leaves Atlanta for Philadelphia at 2pm traveling 60 mph. The distance from Philadelphia to Atlanta is 400 miles. Where d the trains meet? When do they meet? sol : suppose they meet x hrs after 12. then dist moved by first in x hrs + dist moved by second in (x - 1) hrs = 400 70 x + 60(x-2) = 400 solving for x you come to know 4 hrs after the 12.
 Travel_Word_Problems/576068: A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is th speed of the motorboat? (Assume that the motorboat maintains a constant speed relative to the water.)1 solutions Answer 369778 by chana(69)   on 2012-02-22 10:21:40 (Show Source): You can put this solution on YOUR website!A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is th speed of the motorboat? let the speed of the boat = x speed of boat in upstream = x - 3 speed of boat in downstream = x + 3 distance = speed * time so (x - 3)* 5 = (x + 3) * 2.5 solve for x to get the speed of the boat .
 Linear-systems/576155: A club offers single memberships, couple memberships, and family memberships. The club has sold a total of 1530 memberships. The couple memberships are 38 more than twice the single memberships. The family memberships are 8 less than three times the single ones. Use s, c, and f to represent single, couple, and family memberships respectively and write a system of three equations that describes this problem. Solve the system to find the number of memberships in each category. Answer: the club has sold ………. single memberships, …….. couple memberships, and ……………. family memberships. 1 solutions Answer 369772 by chana(69)   on 2012-02-22 10:09:03 (Show Source): You can put this solution on YOUR website!A club offers single memberships, couple memberships, and family memberships. The club has sold a total of 1530 memberships. The couple memberships are 38 more than twice the single memberships. The family memberships are 8 less than three times the single ones sol : as given : s + c + f = 1530 ----(1) c = 38 +2s ---------(2) f = 3s - 8 ---------(3)substituting 2& 3in equation 1 you can get the required value which gives s =300 , f = 892 , c = 338
 Permutations/576163: Seven students applied for a position on the four-member student review board. In how many ways could four students have been selected for the board? please show me the steps. 1 solutions Answer 369770 by chana(69)   on 2012-02-22 10:03:23 (Show Source): You can put this solution on YOUR website!Seven students applied for a position on the four-member student review board. In how many ways could four students have been selected for the board? sol : (4 from 7) so total ways = 7c4 =(7*6*5*4)/(4*3*2*1) = 35 ways
 Probability-and-statistics/576173: In how many ways can we select a class president from a group of 4 scholars, a secretary from a group of 3 girls and an adviser from a group of 3 professors?1 solutions Answer 369769 by chana(69)   on 2012-02-22 10:01:11 (Show Source): You can put this solution on YOUR website!In how many ways can we select a class president from a group of 4 scholars, a secretary from a group of 3 girls and an adviser from a group of 3 professors? sol : (1 from 4) * (1 from 3) * (1 from 3) so 4c1 * 3c1 * 3c1 = 36 ways