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# Recent problems solved by 'MathTherapy'

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 Linear_Equations_And_Systems_Word_Problems/726757: Jenny buys three apples and five lemons for \$8.50, while a second shopper buys six apples and four lemons for \$9,86. What is the price of each fruit? 1 solutions Answer 444885 by MathTherapy(1424)   on 2013-03-16 22:16:26 (Show Source): You can put this solution on YOUR website!Jenny buys three apples and five lemons for \$8.50, while a second shopper buys six apples and four lemons for \$9,86. What is the price of each fruit? Cost of 1 lemon: \$ Cost of 1 apple: \$
 Triangles/723099: I have another question. Given that the measure of angle a= 74 degrees and the measure of angle b= 52 degrees, find the measure of angles x and y. In the drawing, angle x is on the lower right interior of the triangle and angle y is on the lower right exterior of the triangle. I am so totally lost...please help... Becky1 solutions Answer 443048 by MathTherapy(1424)   on 2013-03-07 11:42:42 (Show Source): You can put this solution on YOUR website! I have another question. Given that the measure of angle a= 74 degrees and the measure of angle b= 52 degrees, find the measure of angles x and y. In the drawing, angle x is on the lower right interior of the triangle and angle y is on the lower right exterior of the triangle. I am so totally lost...please help... Becky Based on your description, x seems to be the third angle of the triangle, while y appears to be one of the exterior angles of the triangle, formed by extending one of the triangle's sides. As the angles of a triangle sum to , we can say that x = 180 - (a + b), or x = 180 - (74 + 52), or x = 180 - 126, or As the angles on a straight line are SUPPLEMENTARY (sum to ), and as x and y are on a straight line, we can say that x + y = 180. Now, since x = , then 54 + y = 180 ----- y = 180 - 54, or OR As any exterior angle, formed by extending one side of a triangle, is the sum of the two opposite interior angles, we can say that: y = a + b, or y = 74 + 52, or Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Triangles/723098: One angle of a triangle is 15 degrees more than the measure of the second angle. The third angle is 15 degrees less than the measure of the second angle. Find the measure of each angle. I am having a really hard time with geometry...I was bad at it 20 + years ago and it hasn't gotten any better since then. If anyone can show me how to figure this out I would really appreciate it! :) Becky1 solutions Answer 443045 by MathTherapy(1424)   on 2013-03-07 11:30:22 (Show Source): You can put this solution on YOUR website! One angle of a triangle is 15 degrees more than the measure of the second angle. The third angle is 15 degrees less than the measure of the second angle. Find the measure of each angle. I am having a really hard time with geometry...I was bad at it 20 + years ago and it hasn't gotten any better since then. If anyone can show me how to figure this out I would really appreciate it! :) Becky Let second angle's measure be S Then first angle's measure = S + 15 Third angle's measure = S - 15 As the angles of a triangle sum to , we can say that: S + S + 15 + S - 15 = 180 3S = 180 S, or second angle's measure = , or First angle's measure = 60 + 15, or Third angle's measure = 60 - 15, or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Percentage-and-ratio-word-problems/722984: If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59. Let the fraction be ab. Write down two equations satisfied by a and b: (i) (ii) Find the fraction. ab1 solutions Answer 443012 by MathTherapy(1424)   on 2013-03-07 01:47:43 (Show Source): You can put this solution on YOUR website! If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59. Let the fraction be ab. Write down two equations satisfied by a and b: (i) (ii) Find the fraction. ab ---- 35b + 35 = a + 1 ----- a – 35b = 34 ---- eq (i) ---- 59b – 59 = a – 1 ----- a – 59b = - 58 ---- eq (ii) Solving, a = , and b = You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 test/722996: Identify the number that satisfies all three of the following conditions:  it is a composite between 62 and 72;  the sum of the digits is a prime number; and  it has more than four factors.1 solutions Answer 443008 by MathTherapy(1424)   on 2013-03-07 01:23:57 (Show Source): You can put this solution on YOUR website!Identify the number that satisfies all three of the following conditions:  it is a composite between 62 and 72;  the sum of the digits is a prime number; and  it has more than four factors. Number is Factors: 2, 5, 7, 10, 14, 35, 70 (more than 4, so COMPOSITE, since it has more than 1 pair of factors) Sum of digits: 7 + 0, or 7 (prime)
 Polynomials-and-rational-expressions/722920: How do I solve (4/b^2)=(1/b^2)-(2/b)?1 solutions Answer 443004 by MathTherapy(1424)   on 2013-03-07 01:00:47 (Show Source): You can put this solution on YOUR website!How do I solve (4/b^2)=(1/b^2)-(2/b)? 4 = 1 - 2b ------ multiplying by LCD, 4 - 1 = - 2b 3 = - 2b b = , or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 test/721820: I need t o find a math tutor1 solutions Answer 442538 by MathTherapy(1424)   on 2013-03-04 18:11:09 (Show Source): You can put this solution on YOUR website!I need t o find a math tutor You can E-Mail me at MathMadEzy@aol.com, and I'll see what I can do for you. I charge a fee though.
 Miscellaneous_Word_Problems/720796: Buffalo contributed 6 more tons of clothing to a drive than did Troy. Endicott contributed half as much as Troy. In all they continued 71 tons. How many tons were contributed by each?1 solutions Answer 442029 by MathTherapy(1424)   on 2013-03-01 23:51:32 (Show Source): You can put this solution on YOUR website! Buffalo contributed 6 more tons of clothing to a drive than did Troy. Endicott contributed half as much as Troy. In all they continued 71 tons. How many tons were contributed by each? Let amount contributed by Troy be T Then amount contributed by Buffalo = T + 6 Amount Endicott contributed = ˝ * T, or Therefore, 4T + 12 + T = 142 ------ Multiplying by LCD, 2 5T = 130 T, or Troy contributed , or tons Buffalo contributed 26 + 6, or tons Endicott contributed ˝ * 26, or tons You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Age_Word_Problems/720459: The question reads name 3 solutions forbthe inequality then graph on number line the equation says p is greater than 18. This is my grandson math question and I need help I can't figure it out?1 solutions Answer 441871 by MathTherapy(1424)   on 2013-02-28 22:36:20 (Show Source): You can put this solution on YOUR website! The question reads name 3 solutions forbthe inequality then graph on number line the equation says p is greater than 18. This is my grandson math question and I need help I can't figure it out? Since p > 18, any 3 numbers that are GREATER tan 18 can be solutions, so choose any 3 such numbers. Draw a number line. Place an OPEN CIRCLE on the line at the point that's represented by the number 18. Then draw a very, very BOLD arrow pointing to the right of the number 18 on the number line to indicate that the solutions are numbers that are GREATER than 18. That's it!!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Proportions/720467: how do I solve 2/t = t/-5-121 solutions Answer 441866 by MathTherapy(1424)   on 2013-02-28 22:19:28 (Show Source): You can put this solution on YOUR website! how do I solve 2/t = t/-5-12 ----- Multiplying by LCD, - 5t Solving using the quadratic equation, t = , or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Miscellaneous_Word_Problems/720506: If twice B is eighteen less than five times B, what is the value of B?1 solutions Answer 441862 by MathTherapy(1424)   on 2013-02-28 22:10:24 (Show Source): You can put this solution on YOUR website! If twice B is eighteen less than five times B, what is the value of B? 2B = 5B - 18 Solve for B to get a value of: You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Angles/716555: the supplement of an angle is 10 less than three times its complement. what is the measure of the angle?1 solutions Answer 439943 by MathTherapy(1424)   on 2013-02-20 13:12:33 (Show Source): You can put this solution on YOUR website!the supplement of an angle is 10 less than three times its complement. what is the measure of the angle? Let the angle's measure be A Then its supplement is 180 - A, and its complement is: 90 - A Therefore, 180 - A = 3(90 - A) - 10 180 - A = 270 - 3A - 10 - A + 3A = 270 - 10 - 180 2A = 80 A, or measure of angle = , or You can do the check You can send "thank yous" to D at MathMadEzy@aol.com
 Linear-systems/712485: x+4/ (x^2-3x+2) - 5/(x^2-4x+3) = x-4/ (x^2-5x+6)1 solutions Answer 438001 by MathTherapy(1424)   on 2013-02-09 16:49:23 (Show Source): You can put this solution on YOUR website!x+4/ (x^2-3x+2) - 5/(x^2-4x+3) = x-4/ (x^2-5x+6) You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Age_Word_Problems/712175: Dave is twice as old as Rick. Ten years ago the sum of their ages was 40. How old are they now?1 solutions Answer 437857 by MathTherapy(1424)   on 2013-02-08 19:52:42 (Show Source): You can put this solution on YOUR website! Dave is twice as old as Rick. Ten years ago the sum of their ages was 40. How old are they now? Let Rick's current age be R Then Dave's current age = 2R Ten years ago, Rick was R - 10, and Dave was: 2R - 10 Therefore, R - 10 + 2R - 10 = 40 3R - 20 = 40 3R = 60 R, or Rick's current age = , or Dave's current age = 2(20), or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 decimal-numbers/701770: I need help with my math homework on decimals : Decimal patterns with powers of 10.Divide 4 divided by 0.51 solutions Answer 432583 by MathTherapy(1424)   on 2013-01-13 23:11:27 (Show Source): You can put this solution on YOUR website!I need help with my math homework on decimals : Decimal patterns with powers of 10.Divide 4 divided by 0.5 When dividing decimals, you first need to convert the divisor, or the denominator (0.5 in this case) to a WHOLE number. This is attained by moving the decimal point one place to the right (this is the same as multiplying the divisor or denominator by 10), therefore leading to a divisor or denominator of 5. Now, since the divisor's decimal point was moved 1 place to the right to make it a WHOLE number, we also need to move the decimal point in the NUMERATOR, one place to the right(this is the same as multiplying the numerator by 10). This gives us 40 as the numerator. We now have: , which gives us: You can then check this answer on a calculator, if you're allowed to use one. Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Triangles/701683: I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse?1 solutions Answer 432572 by MathTherapy(1424)   on 2013-01-13 21:57:42 (Show Source): You can put this solution on YOUR website!I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse? When the longer leg of a 30-60-90 triangle is known, its shorter leg = , or in this case: ----- ---- ----- ----- ----- , or When the longer leg of a 30-60-90 triangle is known, its hypotenuse = , or in this case: , or , or 2 *19.05255888 ≈ You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Rational-functions/701287: how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25) 1 solutions Answer 432388 by MathTherapy(1424)   on 2013-01-12 22:42:51 (Show Source): You can put this solution on YOUR website! how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25) ______**Note: x(x + 5) - 2(x - 5) = 50 ------ Multiplying by LCD, (x - 5)(x + 5), or (x - 5)(x + 8) = 0 x = 5 (ignore as as stated earlier) You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Quadratic_Equations/699533: I need steps and answer! Thanks!1 solutions Answer 431461 by MathTherapy(1424)   on 2013-01-08 15:32:17 (Show Source): You can put this solution on YOUR website! I need steps and answer! Thanks! **Note: , or , as these values would render the equation UNDEFINED x - 1 + x(x - 3) = 2(x - 2) ------ Multiplying by LCD, , or (x - 2)(x - 3) (x - 3)(x - 1) = 0 x - 3 = 0 ------ x = 3 (ignore as it was stated before that: ) OR x - 1 = 0 ----- You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Travel_Word_Problems/699608: solution of root over 50=root over 25+x square1 solutions Answer 431454 by MathTherapy(1424)   on 2013-01-08 14:11:24 (Show Source): You can put this solution on YOUR website! solution of root over 50=root over 25+x square ------ Taking the square root of each side x = ± You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 test/699470: A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number.1 solutions Answer 431412 by MathTherapy(1424)   on 2013-01-08 02:32:25 (Show Source): You can put this solution on YOUR website! A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number. Since number is between 300 and 400, then the hundreds digit MUST be 3 Let the tens, and units digits be T, and U, respectively Then: 300 + 10T + U = 40(3 + T + U) 300 + 10T + U = 120 + 40T + 40U 10T – 40T + U – 40U = 120 – 300 - 30T – 39U = - 180 - 3(10T + 13U) = - 3(60) 10T + 13U = 60 ------ eq (i) T = U + 6 ------ eq (ii) 10(U + 6) + 13U = 60 --------- Substituting U + 6 for T in eq (i) 10U + 60 + 13U = 60 23U = 0 U, or units digit = 0 T = 0 + 6 ------ Substituting 0 for U in eq (ii) T, or tens digit = 6 Three-digit number between 300 and 400 = You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Graphs/699489: I would greatly appreciate your help in solving this equation for my 12 year old son. The answer must be solved and graphed. -4(-4 + x) > 56 graph is as follows: -14 -12 -10 -8 -6 -41 solutions Answer 431407 by MathTherapy(1424)   on 2013-01-08 01:12:28 (Show Source): You can put this solution on YOUR website! You can do the check!! Draw an OPEN CIRCLE on the number-line graph at - 10, along with an EXTREMELY BOLD arrow pointing to the left of - 10. This indicates that x is any value that is less than - 10. Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Graphs/699491: I would greatly appreciate your help in solving this equation for my 12 year old son. The answer must be solved and graphed. -4(3 + n)> -32 The graph is as follows: 1 2 3 4 5 6 7 8 9 10 11 1 solutions Answer 431406 by MathTherapy(1424)   on 2013-01-08 01:10:41 (Show Source): You can put this solution on YOUR website!I would greatly appreciate your help in solving this equation for my 12 year old son. The answer must be solved and graphed. -4(3 + n)> -32 The graph is as follows: 1 2 3 4 5 6 7 8 9 10 11 - 4(3 + n) > - 32 - 12 - 4n > - 32 - 4n > - 32 + 12 - 4n > - 20 ----- Inequality changes from > to < when dividing by a value < 0 (negative value) You can do the check!! Draw an OPEN CIRCLE on the number-line graph at 5, along with an EXTREMELY BOLD arrow pointing to the left of 5. This indicates that n is any value that is less than 5. Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Trigonometry-basics/698954: Solve (x-3)^2=25 by using the Quadratic Formula. Step by step answers. Thanks!!!!!!!!1 solutions Answer 431157 by MathTherapy(1424)   on 2013-01-06 21:00:21 (Show Source): You can put this solution on YOUR website!Solve (x-3)^2=25 by using the Quadratic Formula. Step by step answers. ----- Using the quadratic equation, a = 1; b = - 6; c = - 16. When solved, you should get: x = 8, or - 2, as seen from the shortcut below. ----- Taking the square root of both sides x - 3 = ± 5 x - 3 = 5 ----- x = 5 + 3, or OR x - 3 = - 5 ---- x = - 5 + 3, or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Money_Word_Problems/698913: Hi. I kind of understand how a total salary amount over a certain period of years with a fixed annual increase using arithmetic series is done but how does one do this if the annual rate of increase is a percentage? e.g. What would be the total amount of a salary that starts at \$20,000 per year at an annual increase of 5% over 10 years? Thank you. Paul Stone1 solutions Answer 431151 by MathTherapy(1424)   on 2013-01-06 20:44:10 (Show Source): You can put this solution on YOUR website! Hi. I kind of understand how a total salary amount over a certain period of years with a fixed annual increase using arithmetic series is done but how does one do this if the annual rate of increase is a percentage? e.g. What would be the total amount of a salary that starts at \$20,000 per year at an annual increase of 5% over 10 years? Thank you. Paul Stone This is the equivalent of asking one to determine the future value, after 10 years, of \$20,000, which is compounded annually, at a rate of 5%. The future value formula, can be used, with A being the future value, or value after 10 years, P = present value, or \$20,000, r = rate of interest, or 5% (.05), m being the amount of compounding periods per year, and t being the time, in years (10) Therefore, becomes: ----- A, or amount in 10 years = 20000(1.628894627), or \$ You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Mixture_Word_Problems/698482: I a on a diet and need some converting help. I used to know a way to do this algebraically. If four ounces has 13 grams of protein, how much protein does one ounce have? Can you tell me a way to set up the problem and what to do....I will need to do this with a lot of things. Thank you so much. Shelley1 solutions Answer 430765 by MathTherapy(1424)   on 2013-01-05 02:04:20 (Show Source): You can put this solution on YOUR website! I a on a diet and need some converting help. I used to know a way to do this algebraically. If four ounces has 13 grams of protein, how much protein does one ounce have? Can you tell me a way to set up the problem and what to do....I will need to do this with a lot of things. Thank you so much. Shelley The easiest way is to set up these types of problems as PROPORTIONS This can be set up as: , or This will give you: , or , with G being the amount of grams of protein You then cross-multiply to get: 4P = 13 , or grams of protein You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Linear_Equations_And_Systems_Word_Problems/698487: What are three consecutive whole numbers whose sum is 48?1 solutions Answer 430763 by MathTherapy(1424)   on 2013-01-05 01:51:59 (Show Source): You can put this solution on YOUR website! What are three consecutive whole numbers whose sum is 48?
 Linear_Algebra/698504: 2x-1/x=3/4 find x.1 solutions Answer 430760 by MathTherapy(1424)   on 2013-01-05 01:37:11 (Show Source): You can put this solution on YOUR website! 2x-1/x=3/4 find x. Is it too strenuous or too difficult to use parentheses to make the problem clearer? If it's (2x - 1)/x = 3/4, then , but 4(2x - 1) = 3x ------ Cross-multiplying 8x - 4 = 3x 8x - 3x = 4 5x = 4 You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Complex_Numbers/698121: 3-5i/5+2i1 solutions Answer 430578 by MathTherapy(1424)   on 2013-01-03 21:54:45 (Show Source): You can put this solution on YOUR website! 3-5i/5+2i ------ ----- ----- ------ ----- ---- Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Money_Word_Problems/698063: How do you set up the equation to solve the problem, "A merchant wants to clear \$365.00 after paying a service fee of 3.25%. How much much must the merchant charge his customer?" I multiplied \$365.00 by 0.0325, then added that amount to the \$365.00. Is there a better method/formula, Please. Thank you.1 solutions Answer 430428 by MathTherapy(1424)   on 2013-01-03 01:41:15 (Show Source): You can put this solution on YOUR website!How do you set up the equation to solve the problem, "A merchant wants to clear \$365.00 after paying a service fee of 3.25%. How much much must the merchant charge his customer?" I multiplied \$365.00 by 0.0325, then added that amount to the \$365.00. Is there a better method/formula, Please. Thank you. The \$365 represents 100%, so adding 3.25% to 100% results in a multiplicative amount of , which is then multiplied by \$365 (), thus resulting in the amount to be charged to the customer. This amount will also be the same as calculating the 3.25% service fee and then adding it to the \$365 - just as you did. Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 expressions/697504: 18-2[2-3{-2(5-4)}]1 solutions Answer 430170 by MathTherapy(1424)   on 2012-12-31 23:13:27 (Show Source): You can put this solution on YOUR website! 18-2[2-3{-2(5-4)}] 18 - 2[2 - 3{- 2(1)}] 18 - 2[2 - 3{- 2}] 18 - 2[2 + 6] 18 - 2[8] 18 - 16 = Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
 Equations/697578: how do you solve the equation of y-y with the exponent on the bottom of 1 = m( x - xwith the exponent on the bottom of 1) if y is 3 and x is 22? 1 solutions Answer 430169 by MathTherapy(1424)   on 2012-12-31 22:57:10 (Show Source): You can put this solution on YOUR website! how do you solve the equation of y-y with the exponent on the bottom of 1 = m( x - xwith the exponent on the bottom of 1) if y is 3 and x is 22? I guess you're referring to the point-slope formula that says: , with m being the slope. But, solve it for what?