Grandma gives 180 marbles to her ten grandchildren. No two children get the same amount of marbles. Betsy gets the most. What is the least number of marbles that Betsy could get?

23 marbles

Step-by-step explanation:

Number of children = 10

Number of marbles = 180

Since Betsy gets the most and no 2 children gets the same number of marbles

The least number of marbles Betsy could get will be x ; with the other 9 children receiving 1 less each

That is :

Betsy = x

9th child = x - 1

8th child = x - 2,... 1st child = x - 9

Hence,

(x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 + x - 6 + x - 7 + x - 8 + x - 9) = 180

10x - 45 = 180

10x = 180 + 45

x = 225 / 10

x = 22.5

x = 23

Hence, the least Betsy could get is 23 marbles

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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