How many glasses total are there?

[amyjojoja]

the problem reads. 2/7 of the glasses at a restaurant are green. the rest are white. 210 more are white than green. How many glasses total are there.

I was only able to come up with 490 but that was by listing all the factors of 7 and just checking each one until I found that 490 works. any help on how to do this problem quickly and more efficiently would be great.

thanks,

 

[Greg]

Hi amyjojoja and welcome to MHB! :D

Let $T$ be the total number of glasses, let $W$ be the number of white glasses and let $G$ be the number of green glasses:

$$T=W+G=210+2G$$

$$\frac27T=G\Rightarrow\frac27T=\frac{T-210}{2}\implies T=490$$