The following proportion is read as "twenty is to twenty-five as four is to five." In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion.To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.Solution: Let the number of chocolates be 5x and the number of ice-cream cones be 8x. Therefore, number of ice-cream cones in the box = 8*6 = 48.
Let us take a look at some examples: Question: In a mixture of 45 litres, the ratio of sugar solution to salt solution is 1:2.
What is the amount of sugar solution to be added if the ratio has to be 2:1?
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 $150, find the total amount and the money received by Ron and Sam.
We can divide both sides of the equation by the same number, without changing the meaning of the equation.
When we divide both sides by 20, we find that the building will appear to be 75 feet tall.A 30-inch tall model building was also used in the movie. First, write the proportion, using a letter to stand for the missing term.We find the cross products by multiplying 20 times x, and 50 times 30. Study this step closely, because this is a technique we will use often in algebra.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.a, d are called the extremes and b, c are called the means.For a proportion a:b = c:d, product of means = product of extremes → b*c = a*d.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.If the number of ‘A’ blocks is 50 more than the number of ‘C’ blocks, what is the number of ‘B’ blocks?Solution: Let the number of the blocks A, B, C, D be 4x, 7x, 3x and 1x respectively 4x = 3x 50 → x = 50. Question: If the ratio of chocolates to ice-cream cones in a box is 5:8 and the number of chocolates is 30, find the number of ice-cream cones.