A bag is filled with yellow and orange marbles. There are 97 marbles in the bag. If there are 25 more
yellow marbles than orange marbles, find the number of yellow marbles and the number of orange
marbles in the bag.
Step 1: Let's assume the number of orange marbles be x.
Step 2: According to the problem, there are 25 more yellow marbles than orange marbles. So, the number of yellow marbles will be x + 25.
Step 3: The total number of marbles is given as 97. So, we can write the equation as:
x + (x + 25) = 97
Step 4: Simplify the equation:
2x + 25 = 97
2x = 97 - 25
2x = 72
Step 5: Solve for x:
x = 72/2
x = 36
Step 6: Substitute the value of x back into the equation to find the number of yellow marbles:
x + 25 = 36 + 25
x + 25 = 61
Therefore, there are 36 orange marbles and 61 yellow marbles in the bag.
To find the number of yellow marbles and orange marbles in the bag, we can set up a system of equations based on the given information.
Let's assume the number of orange marbles in the bag is represented by 'x'. According to the given information, the number of yellow marbles is 25 more than the number of orange marbles. So, the number of yellow marbles can be represented by 'x + 25'.
The total number of marbles in the bag is given as 97. So, the sum of the number of yellow marbles and orange marbles should be equal to 97.
Based on these assumptions, we can write the following equations:
x + (x + 25) = 97
Simplifying the equation, we get:
2x + 25 = 97
Subtracting 25 from both sides, we get:
2x = 72
Dividing both sides by 2, we get:
x = 36
So, the number of orange marbles in the bag is 36.
Substituting this value of x into the equation for the number of yellow marbles, we get:
x + 25 = 36 + 25 = 61
Therefore, the number of yellow marbles in the bag is 61.
In conclusion, there are 36 orange marbles and 61 yellow marbles in the bag.
o = orange marbles
y = yellow marbles
There are 97 marbles in the bag mean:
o + y = 97
There are 25 more yellow marbles than orange marbles mean:
y = o + 25
Now:
o + y = 97
Replace y with o + 25
o + o + 25 = 97
2 o + 25 = 97
2 o = 97 - 25
2 o = 72
o = 72 / 2 = 36
y = o + 25 = 36 + 25 = 61
36 orange marbles and 61 yellow marbles