In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number R of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85? Pick one.
A) 144 B) 189 C) 234 D) 279 E) 309
Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.   Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.   If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.   (10x+18x) &lt; 85.   28x &lt; 85, i.e. 28x &lt;= 84 (Since number of balls cannot be in fraction). Thus, x&lt;=3.   (45x+48x) = 93x.   Max (93x) R(45 +48 )= 
<gadget id="calculator">(45 +48 )</gadget>
<output>93</output>
93x.   Max (93x) R= 279.   Answer is 279.
<result>D</result>
In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number R of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?