One mixture contains 6 fluid ounces of water and 10 fluid ounces of vinegar. A second mixture contains 9 fluid ounces of water and 12 fluid ounces of vinegar. Are the mixtures proportional? If not, how much water or vinegar would u add to the second mixture so that they are proportional?
6/10 ≠ 9/12
Now, do you add water or vinegar? Since
6/10 < 9/12
you must add vinegar, so its ratio diminishes. So, you must solve
9/(12+x) = 6/10
x=3
check: 9/15 = 3/5 = 6/10
To determine if the mixtures are proportional, we need to compare the ratio of water to vinegar in each mixture.
For the first mixture, the ratio of water to vinegar is 6:10, which can be simplified to 3:5 by dividing both numbers by 2.
For the second mixture, the ratio of water to vinegar is 9:12, which can be simplified to 3:4 by dividing both numbers by 3.
Since the ratios are not the same, the mixtures are not proportional.
In order to make the mixtures proportional, we need to adjust the ratio in the second mixture to match that of the first mixture.
To do this, we need to find a common multiple of 5 and 4, which is 20.
To the second mixture, we need to add more water and vinegar in the same ratio as the common multiple.
For the water, we multiply both parts of the ratio by 5, giving us 3 x 5 = 15 fluid ounces.
For the vinegar, we multiply both parts of the ratio by 4, giving us 4 x 4 = 16 fluid ounces.
Therefore, to make the mixtures proportional, we would need to add 6 fluid ounces of water (15 - 9) and 4 fluid ounces of vinegar (16 - 12) to the second mixture.
To determine if the two mixtures are proportional, we need to compare the ratios of water to vinegar.
For the first mixture, the ratio of water to vinegar is 6:10, which can be simplified to 3:5 by dividing both numbers by their greatest common divisor, 2.
For the second mixture, the ratio of water to vinegar is 9:12, which can be simplified to 3:4 by dividing both numbers by their greatest common divisor, 3.
Since the two ratios are not the same, the mixtures are not proportional.
To make the mixtures proportional, we need to adjust either the amount of water or the amount of vinegar in the second mixture.
To do this, we can calculate the missing amount of water or vinegar needed to equalize the ratios:
Ratio of water to vinegar in the first mixture = 3:5
Let's assume x ounces of water and y ounces of vinegar need to be added to the second mixture.
Ratio of water to vinegar in the second mixture after adding = (9 + x):(12 + y)
To make the ratios proportional, the new ratio should be equal to 3:5.
So we can set up the following equation:
(9 + x)/(12 + y) = 3/5
Cross-multiplying, we get:
5(9 + x) = 3(12 + y)
45 + 5x = 36 + 3y
5x - 3y = 36 - 45
5x - 3y = -9
Now we need to find a solution where x and y are both positive since we cannot add negative amounts of a liquid.
To do this, we can try different values for x and y that satisfy the equation until we find a positive solution.