A bag contains 30 red marbles and 15 purple marbles. Mr. Clark wants to add 180 marbles to the bag. He wants the ratios or red to purple marbles to remain the same. How many of each should he add?(1 point)
Responses
120 red marbles and 60 purple marbles
100 red marbles and 80 purple marbles
80 red marbles and 100 purple marbles
60 red marbles and 120 purple marbles
In the bag, the ratio of red marbles to purple marbles is 30:15, which can be simplified to 2:1.
Let's assume Mr. Clark adds x red marbles and y purple marbles to the bag.
We can set up the equation:
(x+30)/(y+15) = 2/1
Cross-multiplying:
2(x+30) = 1(y+15)
Expanding:
2x + 60 = y + 15
Rearranging:
2x - y = -45
Since we know that Mr. Clark wants to add a total of 180 marbles, we can also set up the equation:
x + y = 180
Using substitution, we can solve for x:
2x - (180 - x) = -45
2x - 180 + x = -45
3x - 180 = -45
3x = 135
x = 45
Substituting the value of x into the equation x + y = 180:
45 + y = 180
y = 180 - 45
y = 135
Based on these calculations, Mr. Clark should add 45 red marbles and 135 purple marbles to the bag.
Therefore, the correct answer is:
60 red marbles and 120 purple marbles.