to identical jars are filled with equal amount of marbles. the marbles are coloured red or white. the ratio of red to white marblesis 7:1 in jar 1 and 9:1 in jar 2. if there are 90 white marbles altogether, determine the number of red marbles in jar 2.

In jar 1, 1/8 of the marbles are white.

In jar 2, 1/10 of the marbles are white.
Since the jars are filled with an equal amount of marbles, take this value to be x. Therefore, x/8 + x/10 should equal to 90, the total number of white marbles.
From this, we get x = 400 marbles altogether.
This means 200 marbles in each jar.
In jar 2, 9/10 of the marbles are red. There are 200 marbles in this jar. (9/10)*200 = 180 red marbles in jar 2.

how did you get x to equal 400

By solving the equation x/8 + x/10 = 90.

Sorry for the late response.

To determine the number of red marbles in jar 2, we need to find the total number of marbles in jar 2. Let's break down the solution step by step:

1. Let's assume that the number of red marbles in jar 1 is represented by "7x" and the number of white marbles in jar 1 is represented by "x" (since the ratio is 7:1).
This means that the total number of marbles in jar 1 is 7x + x = 8x.

2. Since the number of red marbles in jar 2 is in the ratio 9:1, we can represent it as "9y". Let's find the total number of marbles in jar 2 using this ratio.
The ratio of red to white marbles in jar 2 is 9:1, which means the total ratio is 9+1 = 10.
Therefore, the number of white marbles in jar 2 is (1/10) * 90 = 9.

3. We know that the total number of marbles in jar 2 is 10y (since the ratio is 9:1).
We also know the number of white marbles in jar 2 is 9.
So, the total number of marbles in jar 2 is 9 + 10y.

4. Now, we have two equations:
a) The total number of marbles in jar 1: 8x
b) The total number of marbles in jar 2: 9 + 10y

5. Since both jars are filled with an equal number of marbles, the total number of marbles in jar 1 must be equal to the total number of marbles in jar 2.
Therefore, we can equate these two equations:
8x = 9 + 10y

6. Since we're interested in finding the number of red marbles in jar 2, we need to solve this equation to get the value of y.
Rearranging the equation:
10y = 8x - 9
y = (8x - 9) / 10

7. Since we know the number of white marbles in jar 2 is 9, we can set up another equation:
9 = (1/10) * 90
9 = 9

8. By substituting the value of y back into the equation in step 6, we get:
9 = (8x - 9) / 10

9. Solving this equation, we can multiply both sides by 10:
90 = 8x - 9

10. Adding 9 to both sides to isolate 8x:
90 + 9 = 8x
99 = 8x

11. Dividing both sides by 8 to solve for x:
x = 99 / 8 = 12.375

12. Since x represents the number of white marbles in jar 1, we need to find the number of red marbles in jar 2:
9 + 10y = 9 + 10(12.375)
9 + 10y = 9 + 123.75
10y = 123.75
y = 123.75 / 10 = 12.375

Therefore, the number of red marbles in jar 2 is 10 * 12.375 = 123.75 (or approximately 124 red marbles).