A bag is filled with green and blue marbles. There are 101 marbles in the bag. If there are 25 more green marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.
g = b+25
b+g = 101
656
Let's assume the number of blue marbles in the bag is "x".
According to the given information, the number of green marbles is 25 more than the number of blue marbles, so the number of green marbles can be expressed as "x + 25".
The sum of the blue and green marbles should be equal to the total number of marbles, which is 101. Therefore, we can set up the equation:
x + (x + 25) = 101
Simplifying the equation:
2x + 25 = 101
Subtracting 25 from both sides:
2x = 101 - 25
2x = 76
Dividing both sides by 2:
x = 38
So, there are 38 blue marbles in the bag.
Substituting the value of x into the equation for the number of green marbles:
x + 25 = 38 + 25 = 63
Therefore, there are 63 green marbles in the bag.
In summary, the bag contains 38 blue marbles and 63 green marbles.
To solve this problem, let's use algebra.
Let's represent the number of blue marbles in the bag as "x". Since there are 25 more green marbles than blue marbles, we can represent the number of green marbles as "x + 25".
According to the information given, the total number of marbles in the bag is 101. So, the equation representing this situation is:
x + (x + 25) = 101
Now, let's solve the equation:
2x + 25 = 101 (combining like terms)
2x = 101 - 25 (subtracting 25 from both sides)
2x = 76
Dividing both sides of the equation by 2, we get:
x = 76 / 2
x = 38
Therefore, there are 38 blue marbles in the bag.
To find the number of green marbles, we substitute the value of x into the expression x + 25:
38 + 25 = 63
Therefore, there are 63 green marbles in the bag.
In conclusion, there are 38 blue marbles and 63 green marbles in the bag.