Question

Abag contains red, geen. and blue marties Ono-sldhofthe mables are red, thern aroǐas many blue maties n geen marbles"dthw"o 15 tme red marbles than green marbles Determine the number of marbles in the bag in these two spproaches (a) Use algebraic reasoning (le, Introduce variables fom equations, and then solve the equations) (b) Use the set model of fractions, labeling a Venn dagram (o) There arered marbles,gren marbles, and bloe matbles

Answer 1

a) Let R,B,G denote the number of red,blue and green marbles respectively. let T be the total number of marbles.

According to the given problem,

T/6 = R => T =6R ....(1) ,

B = G/4 => G = 4B.....(2),

G-R=15 => R = G - 15....(3)

R+B+G=T ...(4)

substituting (1) in (4) we get, R + B + G = 6R => B + G = 5R, , substituting R from eqn.(3), we get B + G = 5(G - 15)

putting G= 4B we get, => B + 4B = 5 (4B - 15)

=> 5B = 5(4B - 15) => B = 4B - 15 => 3B = 15 => B=5

putting B=5 in (2), we get G=20

puting G=20 in (3) we get R = 20-15 = 5

Therefore there are 5 red marbles, 20 green marbles and 5 blue marbles.

b)

set model of fractions for the number of red, blue and green marbles Red Blue