Question

3/5 of the balls in a box are red. The rest are green and yellow. The ratio of the number of green balls
to the number of yellow balls is 5:3. If there are 10 less yellow balls than green balls, how many red
balls are there?​

Answer 1

Answer:

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Step-by-step explanation:

We know that the ratio between green and yellow balls is 5:3 and there are 10 less yellow balls than green balls.

So it follows from this that for any amount of green balls, there are 3/5 as many yellow balls, and also there are 10 less yellow than green.

From this we may write an equality for the number of yellow balls with green balls as a variable and solve for the number of green balls as follows:

(3/5)*g = g - 10

=> 3*g = 5*g - 50

=> 2*g = 50

=> g = 25.

Since g = 25, then it must be the case from our conditions mentioned above that the number of yellow balls, y=15.

Since green balls and yellow balls added together (g + y = 40) make up 2/5 of the total, it follows that the total number of balls is 100. From this, If 3/5 of the balls are red, then it follows that there are 60 red balls.