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I was wondering if any of you could solve the following equation,

Green paint and yellow paint can be mixed in the ratio 4:7 to make a certain lime colored shade. If a painter has 500 ml of green and 650 ml of yellow, what volume of lime colored paint can be made?

I have tried to solve this by using up all the green paint, and then using what is left of the yellow paint, however, I get confused when I do this. I also tried to add 500 and 650 to make it easier, but this does not work either.

Thank a lot!

Christopher U
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  • For the purpose of making lime green paint, it is the yellow paint that is in short supply. Use it all. – André Nicolas Dec 30 '15 at 23:41
  • Hi, thanks for your reply, I have done that, but what would I do next? – Christopher U Dec 30 '15 at 23:56
  • Either then calculate the amount of green paint used, and add, or more simply multiply $650$ by $\frac{11}{7}$. – André Nicolas Dec 31 '15 at 00:04
  • Where did you get the number 11/7 from? – Christopher U Dec 31 '15 at 00:23
  • If there are $7$ yellow to every $4$ green, for every $7$ yellow we get $11$ of mixture. – André Nicolas Dec 31 '15 at 00:24
  • Hi really sorry to bother you more, but how come you ended up with 11/7 (how did you end up with an improper fraction?) And how come you only use one of the paints, and not both of them I really appreciate your help thank you. – Christopher U Jan 02 '16 at 09:08
  • We use both paints of course, but if we used all of both the result would be too green. So we use $650$ of the yellow and $650$ times $\frac{4}{7}$ green paint, for a total yield of $650+650\cdot \frac{4}{7}$. which is $650\cdot \frac{11}{7}$. – André Nicolas Jan 02 '16 at 09:13

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