Masha had 200 scoops of ice cream and Liz had 180 scoops of ice cream. After they each ate an equal number of scoops, the ratio of the number of scoops that Masha had remaining to number of scoops that Liz had remaining was 3:2. How many scoops did they each eat?

The number of ice cream scoops that both Masha and Liz ate is 140. This answer was found by setting up and solving a proportional equation based on the information provided.

Explanation:

Let's denote the number of scoops both Masha and Liz ate as 'x'. Initially, Masha had 200 scoops and Liz had 180 scoops. After eating 'x' ice-cream scoops, Masha would have (200 - x) scoops left and Liz would have (180 - x) scoops left. The problem provides the ratio of the left scoops as 3:2. So, we can then set up the equation as (200 - x)/ (180 - x) = 3/2. By solving this proportional equation, we can find the value of 'x' which represents how many ice-cream scoops they each ate.

First, cross-multiply to get rid of the fraction: 2*(200 - x) = 3*(180 - x)

Then, simplify and solve for 'x': 400 - 2x = 540 - 3x, x = 140.

So, they each ate 140 scoops of ice cream.

Learn more about Proportional Equations here:

https://brainly.com/question/32231950

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