A bag contains purple marbles and blue marbles, 84 in total. The number of purple marbles is 9 more than 4 times the number of blue marbles. How many purple marbles are there

Answer 1

P = number of purple marbles

B = number of blue marbles

P + B = 84

So B = 84 - P (1)

The number of purple marbles is 9 more than 4 times the number of blue marbles:

P = 4 * B + 9 (2)

Substitute equation (1) into equation (2) to find P:

P = 4 * (84 - P) + 9

P = 336 - 4*P + 9

5 * P = 345

P = 69

Answer 2

b + p = 84

p = 4b + 9

Equal means that we can swap out what's on either side, because they're the same.

b + 4b + 9 = 84

5b + 9 - 9 = 84 - 9

5b = 75

5b/5 = 75/5

b = 15

p = 4(15) + 9 = your answer