In a bag there are a number of red and blue balls. The ratio of red to blue balls is 3:7.
I add 10 balls and the ratio goes to 6:7 red to blue balls.
How many blue balls are there?
3n + 7n = 10n
(3n+10) + 7n = 10n + 10
6n + 7n = 10n + 10
13n = 10n + 10
3n = 10
N = 3.333
7n = 23.333 ( number of blue balls)
original red --- 3x
original blue --- 7x
number of reds added -- a
number of blues added -- 10-a
(3x+a)/(7x + 10-a) = 6/7
42x + 60 - 6a = 21x + 7a
21x - 13a = -60
I think you have something missing in your problem, maybe a typo
We have to know how the 10 balls are distributed by colour, were they all red? or what ?
Your opening equation is true for all values of n
you made an error in your 3rd line and lost one of the 10's , which explains why your answer makes no sense
Also how did your 3n suddenly become 6n ?
I did miss a bit. The 10 additional balls were all red.
then
(3x+10)/(7x) = 6:7
42x = 21x + 70
21x=70
x = 70/21 = 10/3
so the number of reds originally was 3(10/3) = 10
the number of blues originally was 7(10/3) = 70/3 ?????
how can we have partial balls ?
I think there is something very wrong with your question.
notice that "mathematically" my answer is correct
check:
original reds = 10
original blues = 70/3
10 : 70/3
= 30:70
= 3:7
new reds = 20
blues = 70/3
20:70/3
= 60:70
= 6:7
To solve this problem, we need to set up a system of equations using the given information. Let's assume the number of red balls is represented by "3x" and the number of blue balls is represented by "7x". This means that the ratio of red to blue balls is 3:7.
After adding 10 balls, the total number of balls becomes "10x + 10" since we added 10 balls to the initial number of balls.
We are also given that the new ratio of red to blue balls after adding 10 balls is 6:7. This can be expressed as (3x + 10):(7x) = 6:7.
Now, we can set up the equation:
(3x + 10) / (7x) = 6 / 7
To solve this equation, we can cross-multiply:
7(3x + 10) = 6(7x)
21x + 70 = 42x
Rearranging the equation gives:
21x = 42x - 70
-21x = -70
x = 70/21
x ≈ 3.333
Since we are looking for the number of blue balls, which is represented by "7x", we can substitute the value of x back into the expression to find the number of blue balls:
7(70/21) = 70/3
So, there are approximately 23.333 blue balls in the bag.
Note: It's important to keep in mind that we can't have a fraction of a ball, so we need to round the result. In this case, it would be appropriate to round down since we can't have a fraction of a ball. Therefore, there are approximately 23 blue balls in the bag.