# How many glasses total are there?

• MHB
• amyjojoja
In summary, the total number of glasses at the restaurant is 490, with 210 of them being white and 280 of them being green. To solve this problem efficiently, we can use algebraic equations to represent the given information and solve for the unknown variables.
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,

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:

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

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

## 1. How do you determine the total number of glasses?

This can be determined by counting the number of glasses in a set or collection, or by adding up the number of glasses in each individual package or box.

## 2. Is there a formula for calculating the total number of glasses?

No, the total number of glasses depends on the specific set or collection and cannot be determined by a single formula.

## 3. Does the type of glass affect the total number?

Yes, the size and shape of the glasses can affect the total number. For example, if there are both tall and short glasses in a collection, the total number will be different compared to a collection with only one size of glass.

## 4. Do you include broken glasses in the total count?

No, the total number of glasses refers to the number of intact and usable glasses. Broken glasses should not be included in the count.

## 5. Can the total number of glasses change over time?

Yes, the total number of glasses can change if new glasses are added to the collection or if some glasses are broken or removed from the collection.

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