A bag contains purple marbles and red marbles, 24 in total. The number of purple marbles is 3 less than 2 times the number of red marbles. How many purple marbles are there?
number of reds ---- x
purples ---- 2x - 3
their sum is 24
x + 2x-3 = 24
take over.
Let's assume the number of red marbles as "x". According to the problem, the number of purple marbles is 3 less than 2 times the number of red marbles. So we can write this information as:
Purple Marbles = 2 * Red Marbles - 3
Now, we know that the total number of marbles is 24. So we can set up an equation:
Purple Marbles + Red Marbles = 24
Substituting the value of Purple Marbles from the first equation into the second equation, we get:
(2 * Red Marbles - 3) + Red Marbles = 24
Simplifying the equation:
3 * Red Marbles - 3 = 24
Adding 3 to both sides of the equation:
3 * Red Marbles = 27
Dividing both sides of the equation by 3:
Red Marbles = 9
Therefore, there are 9 red marbles.
Now, substituting this value back into the first equation, we can find the number of purple marbles:
Purple Marbles = 2 * Red Marbles - 3
Purple Marbles = 2 * 9 - 3
Purple Marbles = 18 - 3
Purple Marbles = 15
Therefore, there are 15 purple marbles in the bag.