*The first, second and third terms of the proportion are 42, 36, 35. Solution: We note that 8 × 30 = 240 and 12 × 20 = 240 Thus, 8 × 30 = 12 × 20 ………..(I) Hence, 8 : 12 = 20 : 30 ………..*

*The first, second and third terms of the proportion are 42, 36, 35. Solution: We note that 8 × 30 = 240 and 12 × 20 = 240 Thus, 8 × 30 = 12 × 20 ………..(I) Hence, 8 : 12 = 20 : 30 ………..*(i) We also note that, 8 × 30 = 20 × 12 Hence, 8 : 20 = 12 : 30 ………..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.

We can also use cross products to find a missing term in a proportion. In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long.

However, a model was used for the beetle that was really only 20 inches long.

(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 ………..

(iv) Thus, the required proportions are 8 : 12 = 20 : 30 8 : 20 = 12 : 30 12 : 8 = 30 : 20 12 : 30 = 8 : 20 12. If there are 18 girls in a class, find the number of boys in the class and the total number of students in the class. Solution: Let the third proportional of 16 and 20 be x. This means 16 : 20 = 20 : x So, 16 × x = 20 × 20 x = (20 × 20)/16 = 25 Therefore, the third proportional of 16 and 20 is 25.

Solution: Number of girls in the class = 18 Ratio of boys and girls = 4 : 3 According to the question, Boys/Girls = 4/5 Boys/18 = 4/5 Boys = (4 × 18)/3 = 24 Therefore, total number of students = 24 18 = 42. 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.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.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. For instance, the ratio of number of boys in a class to the number of girls is 2:3.Here, 2 and 3 are not taken as the exact count of the students but a multiple of them, which means the number of boys can be 2 or 4 or 6…etc and the number of girls is 3 or 6 or 9… It also means that in every five students, there are two boys and three girls.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 Ratio And Proportion Problem Solving Examples

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