Ajewel necklace contains only emeralds, rubies, and diamonds. if the ratio of emeralds to diamonds is 2: 7 and the ratio of diamonds to rubies is 3: 2, then which of the following could not be the number of jewels on the necklace? (a) 41(b) 81(c) 82(d) 123(e) 205

B) 81

Step-by-step explanation:

If you have a jewelry necklace with only emeralds, rubies and diamonds (N = R + E + D), If the ratio of emeralds to diamonds is 2: 7 (7E = 2D) and the ratio of diamonds to rubies is 3: 2 (3R = 2D), then which of the following could not be the number of jewels on the necklace? (A) 41 (B) 81 (C) 82 (D) 123 (E) 205

Knowing that:

N=R+E+D; 2D=7E: 2D=3R and 7E=3R Then:

if we begin to substitute the values given in the equation: N = R + E + D, we will observe that for all the values it is fulfilled (whole numbers), but it is only for N = 81 where these values are fractionated

:

FOR N=81    

                    D=(21*81)/41 ≅ 41.487....

                    R=(14*81)/41 ≅ 27.658...

                    E=( 6*81)/41 ≅  1 1.853....

Note: we are told that it ONLY contains rubies, emeralds and diamonds

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation: