# Problem Solving Ratio And Proportion

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One method for solving a proportion problem is to find the appropriate equivalent ratio.

We could have solved the original problem by setting up a proportion and then finding what the equivalent fraction would have to be.

In practice, if we were to actually buy 18 tickets, we may not actually get exactly 3 winning tickets, since this is actually a probability question where the number of tickets could be more or less than 18 tickets, but the average expected number would be 18.

If a beverage company advertices one of every eight bottles of pop wins a free bottle of pop, how many winning bottles would one expect in a gross?

Solution: Sum of the terms of the ratio = 3 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. If x : y = 1 : 2, find the value of (2x 3y) : (x 4y) Solution: x : y = 1 : 2 means x/y = 1/2 Now, (2x 3y) : (x 4y) = (2x 3y)/(x 4y) [Divide numerator and denominator by y.] = [(2x 3y)/y]/[(x 4y)/2] = [2(x/y) 3]/[(x/y) 4], put x/y = 1/2 We get = [2 (1/2) 3)/(1/2 4) = (1 3)/[(1 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9 Therefore the value of (2x 3y) : (x 4y) = 8 : 9 More solved problems on ratio and proportion are explained here with full description.

Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively. If 2A = 3B = 4C, find A : B : C Solution: Let 2A = 3B = 4C = x So, A = x/2 B = x/3 C = x/4 The L. M of 2, 3 and 4 is 12 Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12 = 6x : 4x : 3x = 6 : 4 : 3 Therefore, A : B : C = 6 : 4 : 3 6. Solution: Length of ribbon originally = 30 cm Let the original length be 5x and reduced length be 3x.x = 18', CAPTION, 'One would expect approximately 18 winning bottles in a gross.', CAPTIONSIZE, 2, CGCOLOR, '#006600', PADX, 5, 5, PADY, 5, 5, SHADOW, 0, SHADOWCOLOR, '#c0c0c0', BUBBLECLOSE, STICKY, CLOSECLICK, CLOSETEXT, '', BELOW, RIGHT, BORDER, 1, BGCOLOR, '#006600', FGCOLOR, '#dcffdc', WIDTH, 400, TEXTSIZE, 2, TEXTCOLOR, '#000000', CAPCOLOR, '#FFFFFF');" onfocus="return overlib('x = 18', CAPTION, 'One would expect approximately 18 winning bottles in a gross.', CAPTIONSIZE, 2, CGCOLOR, '#006600', PADX, 5, 5, PADY, 5, 5, SHADOW, 0, SHADOWCOLOR, '#c0c0c0', BUBBLECLOSE, STICKY, CLOSECLICK, CLOSETEXT, '', BELOW, RIGHT, BORDER, 1, BGCOLOR, '#006600', FGCOLOR, '#dcffdc', WIDTH, 400, TEXTSIZE, 2, TEXTCOLOR, '#000000', CAPCOLOR, '#FFFFFF');"A mother of three is pregnant with her fourth child. One evening, the eldest daughter says to her dad: "Dad, do you know what I just found out? If the student attended 15 days, how many days did the summer course run?Note that this time the missing value is in the denominator, since the denominator in the first ratio is days attended to total days. Be Careful with the Wording: We need to watch the wording carefully when working any ratio or proportion problem.(ii) (I) can also be written as 12 × 20 = 8 × 30 Hence, 12 : 8 = 30 : 20 ………..(iii) Last (I) can also be written as 12 : 30 = 8 : 20 ………..Worked out problems on ratio and proportion are explained here in detailed description using step-by-step procedure. Solution: Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.Solved examples involving different questions related to comparison of ratios in ascending order or descending order, simplification of ratios and also word problems on ratio proportion. Then 2x × 50/100 3x × 25/100 4x × 20/100 = 510x/1 3x/4 4x/5 = 510(20x 15x 16x)/20 = 510 ⇒ 51x/20 = 510x = (510 × 20)/51 x = 2002x = 2 × 200 = 400 3x = 3 × 200 = 600 4x = 4 × 200 = 800.What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5? But 5x = 30 cm x = 30/5 cm = 6 cm Therefore, reduced length = 3 cm = 3 × 6 cm = 18 cm More worked out problems on ratio and proportion are explained here step-by-step. Mother divided the money among Ron, Sam and Maria in the ratio 2 : 3 : 5.Solution: Let the number to be added be x, then (2 x) : (3 x) = 4 : 5 ⇒ (2 x)/(5 x) = 4/5 5(2 x) = 4(3 x) 10 5x = 12 4x 5x - 4x = 12 - 10 x = 2 7. If Maria got 0, find the total amount and the money received by Ron and Sam.

## Comments Problem Solving Ratio And Proportion

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