There are only blue sweets, green sweets and red sweets in a box. the ratio of the number of blue sweets to the number of green sweets is 2: 7. the ratio of the number of green sweets to the number of red sweets is 3: 1. there are less than 140 sweets in the box. what is the greatest possible number of red sweets in the box?

The greatest possible number of red sweets is 28.

Explanation:

Let g represent the number of green sweets.  We know that the ratio of blue to green is 2:7; this means the number of blue sweets is 2/7 the number of green sweets, or 2/7g.

We also know that the number of green sweets to the number of red sweets is 3:1; this means the number of red sweets to the number of green sweets is 1:3, or that the number of red sweets is 1/3 the number of green sweets:

1/3g

We know that there are fewer than 140 total sweets; this gives us the inequality

g + 2/7g + 1/3g < 140

We must find a common denominator; 21 will work:

21/21g + 6/21g + 7/21g < 140

34/21g < 140

Divide both sides by 34/21:

(34/21g)÷(34/21) < 140÷(34/21)

g < 140÷(34/21)

To divide fractions, flip the second one and multiply:

g < 140×(21/34)

g < 2940/34

This means the number of red sweets will be 1/3 of this:

r < 2940/34 × 1/3

r < 2940/102

102 will go into 2940 28 times, so 28 is the largest number of red sweets.

answer: 72: 111

step-by-step explanation: