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Beth had a certain number of eggs in her basket. She broke 1/10 of them, gave 6 to her mother and put 3 new eggs in her basket. She then had 24 eggs. how many eggs had she at first

Sagot :

AwesomeHelperidn
Let x be the number of eggs in her basket at first.

x + (- 1/10 - 6 + 3) = 24
x + (- 31/10) = 24
x + (- 31/10) + 31/10 = 24 + (31/10)
x = 271/10 

as a mixed number is 27 and 1/10 eggs.

Check:
She broked 1/10 of them
27 1/10 - 1/10 = 27
Gave 6 to her mother
27 - 6 = 21
Put 3 new eggs in basket.
21 + 3 = 24
There, she had 24 eggs. 
Let the original number of eggs be x.

The number of eggs subtracted from x:
Broken = 1/10 of x
Given to mother = 6
Add them:  x/10 + 6

The number of eggs added to basket: 3 

The eggs left in the basket: 24

Equation:  
x - (x/10 + 6) + 3 = 24
x- x/10- 6 + 3 = 24
x-x/10-3 = 24

LCD: 10.  Multiply each term by 10

(10)x - (10)x/10 - (10)3 = (10) 24
10x -x -30 = 240
9x = 240 + 30
9x = 270
9x/9 = 270/9
x = 30

The number of eggs Beth had at first is 30.

To check:
The eggs subtracted from the basket:
(1/10) of 30 = 3
Eggs given to mother: 6
Total eggs subtracted: 3+6 = 9 eggs

Eggs added:  3
Eggs left:  24

30 - 9 + 3 = 24
21 + 3 = 24
24 = 24

Therefore, Beth had 30 eggs at first.