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?

Answer: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:1/3gWe know that there are fewer than 140 total sweets; this gives us the inequalityg + 2/7g + 1/3g < 140We must find a common denominator; 21 will work:21/21g + 6/21g + 7/21g < 14034/21g < 140Divide 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 < 2940/34This means the number of red sweets will be 1/3 of this:r < 2940/34 × 1/3 r < 2940/102102 will go into 2940 28 times, so 28 is the largest number of red sweets.