sally has a bag with red,blue, and green marbles. She has twice as many blue marbles as red marbles. She has 5 times as many green marbles as red marbles. Altogether she has 24 marbles. How many of each color marble does she have? Explain how you found your answer.
r+b+g=24
g = 5r
b = 2r
r+2r+5r = 24
8r = 24
r=3
so, 3 red, 6 blue, 15 green
To find the number of each color marble Sally has, we can set up a system of equations based on the given information.
Let's assign variables to represent the unknowns:
- Let's say the number of red marbles is "r".
- Since Sally has twice as many blue marbles as red marbles, the number of blue marbles is "2r".
- Since Sally has 5 times as many green marbles as red marbles, the number of green marbles is "5r".
We can then write the following equation based on the total number of marbles:
r + 2r + 5r = 24
Simplifying the equation, we have:
8r = 24
Dividing both sides of the equation by 8, we find:
r = 3
Now that we know the value of "r" (the number of red marbles), we can substitute it back into the equations to find the number of each color marble:
- Number of red marbles = 3
- Number of blue marbles = 2r = 2(3) = 6
- Number of green marbles = 5r = 5(3) = 15
Therefore, Sally has 3 red marbles, 6 blue marbles, and 15 green marbles.