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 Miscellaneous_Word_Problems/659054: Two sailboats are 9.8 miles apart and sailing toward each other. The larger boat sails 4 miles per hour faster than the smaller boat. The two boats pass each other after 0.7 hour. Find the speed of each boat.1 solutions Answer 410621 by josmiceli(9661)   on 2012-09-29 20:24:50 (Show Source): You can put this solution on YOUR website!You can think of one boat as standing still and the other approaching at the sum of their speeds. Let = the speed of the smaller boat = the speed of the larger boat ------------- The speed of the smaller boat is 5 mi/hr The speed of the larger boat is 9 mi/hr
 Miscellaneous_Word_Problems/659057: Paul and Donna Petrie invested \$12,000 part at 5% simple interest and the rest a 7% simple interest for a period of 1 year. How much did they invest at each rate if their total annual interest from both investments was \$800? (Use interest= principal x rate x time.)1 solutions Answer 410616 by josmiceli(9661)   on 2012-09-29 20:12:07 (Show Source): You can put this solution on YOUR website! interest= principal x rate x time Let = amount invested at 5% = amount invested at 7% -------------- ------------------- \$2,000 = amount invested at 5% \$10,000 = amount invested at 7%
 Mixture_Word_Problems/658959: Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. How many quarts of each should be mixed to produce 90 quarts that is 50% alcohol? 1 solutions Answer 410571 by josmiceli(9661)   on 2012-09-29 15:59:46 (Show Source): You can put this solution on YOUR website!Let = quarts of 40% solution needed Let = quarts of 60% solution needed given: (1) (2) -------------------------- (2) (2) (2) -------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) 45 quarts of 40% solution are needed 45 quarts of 60% solution are needed check: (2) (2) (2) (2) (2) OK
 Linear-equations/658968: Where does the equations y=-6x+30 and y=3x-6 intersect? I need the solution. Please HELP ME RIGHT AWAY!1 solutions Answer 410568 by josmiceli(9661)   on 2012-09-29 15:49:00 (Show Source): You can put this solution on YOUR website!Hi These equations are in the slope-intercept form. I would put them into the standard form which looks like Add to both sides (1) and Subtract from both sides Add to both sides Now write it the other way around (2) Add equations (1) and (2) (1) (2) Now plug this result back into (1) or (2) (1) (1) (1) (1) The intersection is at ( 4,6 ) Here's the plot:
 logarithm/658889: knowing that log10((x+y)/3)=1/2(log10(x)+log10(y)) determine the value for x/y P.S - the 3 is inside the log and the log base is 10.1 solutions Answer 410542 by josmiceli(9661)   on 2012-09-29 12:38:36 (Show Source): You can put this solution on YOUR website! Square both sides Divide both sides by Solve for Have to run. Hope I got it.
 Mixture_Word_Problems/658888: A tank holds 140 liters of checmical solution. Currently the solution has a strength of 60%. How much of this should be drained and replaced with 100% solution to get a final strength of 80%?1 solutions Answer 410540 by josmiceli(9661)   on 2012-09-29 12:10:54 (Show Source): You can put this solution on YOUR website!For clarity, I'll just suppose the solution is water plus antifreeze, so it's 60% antifreeze. -------------------- given: liter of antifreeze in 60% solution Let = liters of 60% antifreeze to be drained and repaced with 100% antifreeze ( note there is 140 liters when you start and 140 liters when you finish ) -------------------- 70 liters of solution must be drained and replaced with 100% solution
 Travel_Word_Problems/658752: an airplane flew in a direct line from its base at the rate of 300 miles an hour and returned over the same route at the rate of 250 miles an hour, requiring 15 minutes longer on the return trip. how far from its base did it fly?1 solutions Answer 410463 by josmiceli(9661)   on 2012-09-28 21:46:50 (Show Source): You can put this solution on YOUR website!Let = time for 1st trip Let = distance from base Equation for 1st trip (1) Equation for 2nd trip: (2) ------------------------ Substitute (1) into (2) (2) (2) (2) (2) ------------- (1) (1) (1) It flew 375 mi from base check: (2) (2) (2) (2) (2) OK
 Age_Word_Problems/658400: Taylor is half as old as his father. Next year, their ages will total 62. How old is each now?1 solutions Answer 410274 by josmiceli(9661)   on 2012-09-27 22:06:25 (Show Source): You can put this solution on YOUR website! ---------------------- By substitution: and Taylor is 20 Dad is 40 ---------- check: Next year Taylor is 21 Dad is 41 OK
 Linear_Algebra/658385: Paula is 12 years older than her brother Bob.Four years from now Bob will be two thirds as old as Paula. how old are they now ?1 solutions Answer 410271 by josmiceli(9661)   on 2012-09-27 21:57:30 (Show Source): You can put this solution on YOUR website!Let = Paula's age now Let = Bob's age now given: (1) (2) --------------------------- (2) (2) Substitute (1) into (2) (2) (2) (2) (2) and (1) (1) (1) Paula is 32 Bob is 20 ------------ check: In 4 years Paula is 36 In 4 years Bob is 24 Divide both sides by OK
 Word_Problems_With_Coins/658393: Anna has \$4.00 in change. If she has 5 quarters what is the maximum numbers of dimes that she can have 1 solutions Answer 410269 by josmiceli(9661)   on 2012-09-27 21:46:08 (Show Source): You can put this solution on YOUR website!5 quarters = \$1.25 \$4.00 minus \$1.25 = \$2.75 If she has only 1 nickel, she can have , or \$2.70 which is 27 dimes, which is the maximum
 Age_Word_Problems/658387: Dayna is 8 and her mother is 31. How long will it be before her mother is twice as old as she is? 1 solutions Answer 410266 by josmiceli(9661)   on 2012-09-27 21:40:55 (Show Source): You can put this solution on YOUR website!Add years to both their ages given: In 15 years the Mother's age will be twice the Daughter's check: In 15 yrs Mother is 31 + 15 = 46 In 15 yrs Daughter is 8 + 15 = 23 46 is twice 23 OK
 Mixture_Word_Problems/658364: how many liters of a 10% alcohol solution must be mixed with 70 liters of a 80% solution to get a 60% solution? can you show me how to solve it as well as the answer please? 1 solutions Answer 410261 by josmiceli(9661)   on 2012-09-27 21:10:56 (Show Source): You can put this solution on YOUR website!Let = liters of 10% alcohol solution needed = liters of alcohol in 10% solution liters of alcohol in 80% solution given: 28 liters of 10% alcohol solution are needed check: OK
 Equations/658332: A pet store bought a litter of puppies for \$800. After selling all but 3 puppies in the litter their sales were \$800. Each puppy was sold for \$60 more than they paid for them. How many puppies were in the litter?1 solutions Answer 410259 by josmiceli(9661)   on 2012-09-27 21:00:23 (Show Source): You can put this solution on YOUR website!Let = number of puppies in the litter The store paid for each puppy They sold puppies is the money received per puppy Multiply each side by Looking at this, I can see ( ignore the negative root ) There are 8 puppies in the litter check: They sold all but 3, which is 5 puppies 800/5 = \$160 per puppy 160 - 60 = \$100 This means they paid \$100 for each of the 8 puppies or \$800 OK
 Percentage-and-ratio-word-problems/658336: A trip to the White Mountains of New Hampshire from Boston will take you 2 3/4 hours. Assume you have traveled 1/11 of the way. How much longer will the trip take? 1 solutions Answer 410256 by josmiceli(9661)   on 2012-09-27 20:40:23 (Show Source): You can put this solution on YOUR website!Assuming a fixed speed, the distance traveled is proportional to the time I can set up the proportion hrs The time left is The trip will take 2.5 hours longer
 absolute-value/658270: If you have 2 math grades (88 and 94) and needed to get at least a 90 average, how would you solve this.1 solutions Answer 410235 by josmiceli(9661)   on 2012-09-27 19:19:50 (Show Source): You can put this solution on YOUR website!You do have at least a 90% average You have a 91% average
 Travel_Word_Problems/658264: If Amy can run 3.5 miles in 40 minutes, about how many minutes would it take her to run 8 miles at the same rate? Can you please show me the formula to work this out? 1 solutions Answer 410231 by josmiceli(9661)   on 2012-09-27 19:05:37 (Show Source): You can put this solution on YOUR website! ( time in hours ) mi/hr -------------- hrs It will take her 1 hr 31 min 7 sec
 Linear_Equations_And_Systems_Word_Problems/658204: A roll of carpet 9 ft wide is 30 ft longer than a roll of carpet 15 ft wide. Both rolls have the same area. Make a sketch of the unrolled carpets and find the dimensions of each.1 solutions Answer 410225 by josmiceli(9661)   on 2012-09-27 18:34:43 (Show Source): You can put this solution on YOUR website!Let = the length of the 15' wide carpet given: = the width of the 9' wide carpet Area for each is length x width, so The carpets are 15 x 45 and 9 x 75 ------- check: OK
 Inequalities/658021: A CHEMIST NEEDS TO MIX AN 18% ACID SOLUTION WITH A 45% ACID SOLUTION TO OBTAIN 12 GALLONS OF A 36% ACID SOLUTION. HOW MANY GALLONS OF EACH OF THE ACID SOLUTIONS MUST HE USE? 1 solutions Answer 410113 by josmiceli(9661)   on 2012-09-27 12:30:40 (Show Source): You can put this solution on YOUR website!Let = gallons of 18% solution needed Let = gallons of 45% solution needed given: (1) (2) ----------------------------- (2) (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) ------------- 4 gallons of 18% solution are needed 8 gallons of 45% solution are needed check: (2) (2) (2) (2) OK
 Age_Word_Problems/657990: The mother is 6 years more than three times older than her son. Four years ago, she was 5 times older as her son. How old is her son.1 solutions Answer 410108 by josmiceli(9661)   on 2012-09-27 12:18:39 (Show Source): You can put this solution on YOUR website!Let = Mother's age no Let = Son's age now given: (1) (2) ----------------------- Substitute (1) into (2) (2) (2) (2) (2) (2) Son is 11 check: (1) (1) and (2) (2) (2) (2) OK
 Money_Word_Problems/658002: An adult ticket for the fair (a) is 7 dollars more than a childs ticket which cost 5 dollars, if two adults and three children go to the fair how much will the tickets cost all together? -how do i work this problem out and whats the answer1 solutions Answer 410106 by josmiceli(9661)   on 2012-09-27 12:12:24 (Show Source): You can put this solution on YOUR website!given: Child's ticket = \$5 Adult's ticket = \$5 + 7\$ \$5 + \$7 = \$12 2 adults tickets cost 3 child's tickets cost and All together the tickets cost \$39
 Equations/657799: what are the steps to getting the solutions of this equation 5a^2 - 10a = 0 1 solutions Answer 410008 by josmiceli(9661)   on 2012-09-26 22:40:59 (Show Source): You can put this solution on YOUR website! The solutions are
 Human-and-algebraic-language/657793: if a hen and a half lay an egg and a half, in a day and a half, how many eggs are laid by six hens in six days? show work to explain answer1 solutions Answer 410007 by josmiceli(9661)   on 2012-09-26 22:36:46 (Show Source): You can put this solution on YOUR website!1.5 hens, 1.5 eggs, 1.5 days ------------------------ The same number of hens lay 4 times as many eggs in 4 times as many days 1.5 hens, 6 eggs, 6 days --------------------- 4 times as many hens will lay 4 times as many eggs in the same number of days 6 hens lay 24 eggs in 6 days
 Mixture_Word_Problems/657787: apple pucker is 15% alcohol and vodka is 35% alcohol. how much of each should be mixed to make an 8 oz drink that is 30% alcohol1 solutions Answer 410004 by josmiceli(9661)   on 2012-09-26 22:29:00 (Show Source): You can put this solution on YOUR website!Let = oz of pucker needed Let = oz of vodka needed given: (1) (2) --------------------------- (2) (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and (1) (1) 2 oz of pucker are needed 6 oz of vodka are needed check: (2) (2) (2) (2) OK
 Angles/657781: The ratio of an angle to its supplement is 2:7. What is the ratio of the angle to its ratio to its complement? PLEASE HELP ME ON THIS... T.T1 solutions Answer 410002 by josmiceli(9661)   on 2012-09-26 22:14:16 (Show Source): You can put this solution on YOUR website!Let the angle = It's supplement = given: ---------- answer
 Geometry_Word_Problems/657775: find a rectangle whose perimeter is 22' and has an area that is LARGER than 30'.i come up with 5w x 6l but only equals 30'??1 solutions Answer 409998 by josmiceli(9661)   on 2012-09-26 22:05:20 (Show Source): You can put this solution on YOUR website!A square is a rectangle with equal side Since , and Area = The rectangle is a square with sides = 5.5'
 Distributive-associative-commutative-properties/657397: what is the product of (7x+1/2) and (-10x-22)? i have gotten -70x squared -11 but my teacher told me that was incorrect and i dont know what im doing wrong.1 solutions Answer 409850 by josmiceli(9661)   on 2012-09-26 13:46:20 (Show Source): You can put this solution on YOUR website!The rule is: ( a + b ) x ( c + d ) = ac + bc + ad + bd You got the ac and the bd, but you left out the bc and ad ------------------------- You can check by plugging in some value for x I'll say and, also OK
 Word_Problems_With_Coins/657388: P has pennies, dimes, and quarters. They add up to a total of \$5.59. There are 43 coins and the number of quarters plus 9 equals the number of pennies and dimes. How many quarters? pennies? and dimes does P have? 1 solutions Answer 409848 by josmiceli(9661)   on 2012-09-26 13:34:13 (Show Source): You can put this solution on YOUR website! = number of pennies = number of dimes = number of quarters given: (1) (2) ( in cents ) (3) ------------------- Substitute (3) into (1) (1) (1) (1) ------------- (3) (3) Substitute this back into (2) ----------------- (2) (2) (2) (2) (2) -------------- (1) (1) (1) (1) ------------- P has 14 pennies 12 dimes 17 quarters ----------- check: (2) (2) (2) (2) OK