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.
R1/W1 = 7
R2/W2 = 9
W1 + W2 = 90
R1 + W1 = R2 + W2
Four equations in four unknowns.
Change the last equation by substitution to get rid of R1 and R2.
7W1 + W1= 9W2 + W2
8W1 - 10 W2 = 0
10W1 + 10W2 = 900
18 W1 = 900
W1 = 50
R1 = 350
W2 = 40
R2 = 360
There are 360 red marbles in jar 2
To determine the number of red marbles in jar 2, we can follow these steps:
Step 1: Understand the problem.
We have two identical jars filled with the same amount of marbles. The marbles can be colored either red or white. We know the ratio of red to white marbles in jar 1 is 7:1, and the ratio in jar 2 is 9:1. We also know that there are 90 white marbles in total.
Step 2: Calculate the number of red marbles in jar 1.
Since the ratio of red to white marbles in jar 1 is 7:1, there will be a total of 7 parts of red marbles for every 1 part of white marbles. Hence, we can find the number of red marbles in jar 1 by multiplying the ratio by the number of white marbles:
Number of red marbles in jar 1 = 7 * 90/1 = 630
Step 3: Calculate the number of red marbles in jar 2.
Since the ratio of red to white marbles in jar 2 is 9:1, there will be a total of 9 parts of red marbles for every 1 part of white marbles. We already know that there are 90 white marbles in total. To find the number of red marbles in jar 2, we can multiply the ratio by the number of white marbles:
Number of red marbles in jar 2 = 9 * 90/1 = 810
Therefore, there are 810 red marbles in jar 2.