A bag contains purple marbles and blue marbles, 41 in total. The number of purple marbles is 4 less than 2 times the number of blue marbles. How many purple marbles are there?

There are 26 purple marbles in the bag.

Step-by-step explanation:

1) We have purple (p) and blue (b) marbles in a bag, and 41 marbles total so:

p+b = 41

2) we want to know how many purple marbles we have, so let's rearrange for p:

p = 41 - b

3) Our problem gives us an expression for the purple marbles in terms of the blue, let's write it using math symbols instead of words:

"The number of purple marbles is 4 less than 2 times the number of blue marbles."

so: p = 2b - 4

3) Now we're going to plug this in (or substitute it) for our p in our first equation, and solve for b

p = 41 - b

2b - 4 = 41 - b (substitution)

2b = 45 - b (add 4 to both sides)

3b = 45 (add b to both sides)

b = 15 (divide both sides by 3)

4, last step!)

Now we know we have 15 blue marbles, that's great! But we still want to know how many purple marbles we have.

41 - 15 = 26 purple marbles