Example: A state lottery sells scratch tickets and guarantees that one out of every six tickets is a winning ticket.(a) Express the ratio of winning tickets to losing tickets in simplest form. The ratio of winning tickets to losing tickets is not 1 : 6.(ii) (I) can also be written as 12 × 20 = 8 × 30 Hence, 12 : 8 = 30 : 20 ………..
The correct ratio is 1 : 5, since on average out of six tickets we would expect one winning ticket and five losing tickets.
(b) How many tickets would you expect to have to buy in order for three of them to be winners?
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.
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 this case the numerals representing the number of girls are in the numerators and the numerals representing the number of boys are in the denominators.Example: A student attends only 3 out of every 4 days during a summer course.Since we are looking for the total tickets, we use the ratio of the winning tickets to the total number of tickets, which is 1 : 6.The proportion for the problem would then be To obtain three winning tickets, we would expect to have to buy about 18 tickets.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.I presume you want an equation or method to do the problem. I'm going to tell you how to solve ANY problem. Solution: Let the money received by Ron, Sam and Maria be 2x, 3x, 5x respectively. Therefore, 5x = 150 or, x = 150/5 or, x = 30 So, Ron got = 2x = $ 2 × 30 = Sam got = 3x = 3 × 60 = Therefore, the total amount $(60 90 150) = 0 9. Product of extreme terms = 42 ×x Product of mean terms = 36 X 35 Since, the numbers make up a proportion Therefore, 42 × x = 36 × 35 or, x = (36 × 35)/42 or, x = 30 Therefore, the fourth term of the proportion is 30.Divide 0 into three parts such that second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Solution: Let the first and the third parts be 3x and 5x. = (1/4) × 5x = 5x/4 Therefore, 3x (5x/4) 5x = 370 (12x 5x 20x)/4 = 370 37x/4 = 370 x = (370 × 4)/37 x = 10 × 4 x = 40 Therefore, first part = 3x = 3 × 40 = 0 Second part = 5x/4 = 5 × 40/4 = Third part = 5x = 5 × 40 = $ 200 10. More worked out problems on ratio and proportion using step-by-step explanation. Set up all possible proportions from the numbers 8, 12, 20, 30.