Question

A bag contains purple marbles and blue marbles, 49 in total. The number of purple marbles is 6 less than 4 times the number of blue marbles. How many purple marbles are there?

Answer 1

I know I'm very late but I just wanted to give the answer for future reference. There are 19 purple marbles.

Answer 2

Purple = p

Blue = b

Step 1: Write as an algebraic equation.

p = 4b - 6

p + b = 49

Step 2: Rearrange p + b = 49 to make p the subject.

p + b = 49

p = 49 - b

Step 3: Write p = 4b - 6 and p = 49 - b into one equation.

p = 4b - 6 = 49 - b

Step 4: Move all b values onto one side.

p = 5b = 55

Step 5: Find the value of one blue marble.

5b = 55

b = 11

Step 6: If there are 11 blue marbles and there are 49 marbles in total, then find the number of purple marbles.

p = 49 - b

p = 49 - 11

p = 38

ANSWER:

There are 38 blue marbles.