GIVING BRAINLIEST TO BEST EXPLANATION AND CORRECT ANSWER OPEN DOCUMENT TO FIND QUESTION AND ANSWER!

PLEASE HELP

25 is the answer.

G = green sweets

Ratio of blue to green = 3:5

Ratios are essentially fractions, and can be converted into fraction form

Therefore, number of blue sweets is 3/5 of green sweets, which can also be represented as 3/5g

Number of green sweets to red sweets is 6:1

We can also flip this ratio around and the ratio would still have the same value.

Number of red sweets to green sweets = 1:6

In fraction form, the number of red sweets is 1/6 of green sweets, which is also 1/6g.

Since there are less than 270 sweets in the box, we can use this expression to represent the sweets in the box:

G + 3/5g + 1/6g < 270

Find a common denominator for the fractions.

5 * 6 = 30, thus a common denominator would be 30.

Since G is a variable with no coefficient, 1 would be implied because no coefficient is present.

So when multiplying G to get a common denominator, the numerator would be 30. 30/30 = 1

G * 30 = 1 * 30

G = 30/30g

Multiply the rest of the numerators and you’ll get:

30/30g + 18/30g + 5/30g < 270

Add.

1 + 18/30g + 5/30g = 1 23/30g

Convert this into an improper fraction.

53/30g < 270

Now divide both sides by 53/30.

(53/30g) ÷ (53/30) < 270 ÷ (53/30)

= g < 270 ÷ (53/30)

Dividing fractions is complex, so you can simply switch the numerator and denominator and multiply:

G < 270 x (30/53)

= g < 8,100/53

Since the number of red sweets to green sweets is 1/6g the number of green sweets, the number of red sweets is 1/6 of 8,100/53.

R = red sweets

R < 8,100/53 x 1/6

8,100 x 1 = 8,100

53 x 6 = 318

R < 8,100/318

318 goes into 8,100 25 times, regardless of any remainder.

Therefore, the greatest possible number of red sweets in the box is 25 red sweets.