A bag contains marbles of three different colours red, blue , yellow. 2/5 of the marbles are red. The ratio of the number of blue marbles to the number of yellow marbles is 5:7. What fraction of the marbles in the bag is blue? There are 54 more red marbles than blue marbles. How many marbles are there in the bag?

let the total be x

(2/5)x = r , also b+54 = (2/5)x
b = 2x/5 - 54 = (2x - 270)/5

b : y = 5 : 7
5y = 7b
y = (7/5)b
y = 7(2x-270)/25

so 2x/5 + (2x-270)/5 + 7(2x-270)/25 = x
times 25
10x + 10x - 1350 + 14x - 1890 = 25x
-9x = -3240
x = 360

we have 510 marbles

check:
red = (2/5)(360) = 144
b = (720-270)/5 = 90
y = (7/5)(90) = 126

144+90+126 = 360 , check!
blue : yellow = 90 : 126 = 5 : 7 , check
area there 54 more reds than blues?
144-90 = 54, check!

there are 510 marbles

I obviously got x = 360

So there are 360 marbles,

I have no idea where I got the 510 from, and then I copied it again at the end.
Time for my third cup of coffee.

Let's say there are a total of x marbles in the bag.

Given that 2/5 of the marbles are red, we can calculate the number of red marbles as (2/5) * x = (2x/5).

The ratio of the number of blue marbles to the number of yellow marbles is 5:7. So, we can express the number of blue marbles as (5/12) * total marbles and the number of yellow marbles as (7/12) * total marbles.

It is given that there are 54 more red marbles than blue marbles, so we can set up the equation (2x/5) - (5/12) * x = 54 to solve for x.

Simplifying the equation, we get:
(24/60)x - (25/60)x = 54
(-1/60)x = 54
x = 54 * (-60/1)
x = -3,240

Since the number of marbles cannot be negative, there seems to be an error in the problem statement. Please check the values provided and let me know if there are any corrections.

To find the fraction of marbles that are blue, we need to determine the total number of marbles in the bag and the number of blue marbles specifically.

Let's denote the total number of marbles as "x".
Since 2/5 of the marbles are red, the number of red marbles is (2/5)x.
We are also given that the ratio of blue marbles to yellow marbles is 5:7.
So, we can represent the number of blue marbles as (5/12)x and the number of yellow marbles as (7/12)x.

To find the fraction of marbles that are blue, we divide the number of blue marbles by the total number of marbles:
Fraction of blue marbles = (5/12)x / x = 5/12.

Therefore, the fraction of the marbles in the bag that is blue is 5/12.

Now let's move on to the second part of the question. We are told that there are 54 more red marbles than blue marbles.
So, we can set up the equation (2/5)x - (5/12)x = 54 to find the value of x.

To solve this equation, we need to find a common denominator for the fractions: (24/60)x - (25/60)x = 54.

Simplifying the equation: (-1/60)x = 54.

Dividing both sides by -1/60: x = 54 / (-1/60).

Recall that dividing by a fraction is the same as multiplying by its reciprocal, so x = 54 * (-60/1).

Evaluating the expression: x = -3,240.

Since the number of marbles cannot be negative, we disregard this negative solution.

Therefore, the number of marbles in the bag is 3,240.