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Jan had a bag of marbles. She gave half of them to James and then a third of the marbles still in the bag to pat. She then had 6 marbles left. How many marbles were in the bag to start with?

Respuesta :

bleuberrismoothi14

Answer:

32 marbles

Step-by-step explanation:

Since she only has 6 left, you multiply it by 3 to get the amount she gave to Pat. Then you multiply that number by 2 to get the final amount.

adioabiola

We are required to find the total number of marbles in the bag

The the total number of marbles in the bag is 18

let

Total number of marbles in the bag = x

James = 1/2 of x

= 1/2x

Remaining marbles = x - 1/2x

= 1/2x

Pat = 1/3 of 1/2x

= 1/3 × 1/2x

= 1/6x

Marbles left in the bag = 6

The equation:

Total = James + Pat + marbles left

x = 1/2x + 1/6x + 6

x = (3x + x) / 6 + 6

x = 4x /6 + 6

subtract 4x/6 from both sides

x - 4x/6 = 6

(6x - 4x) / 6 = 6

2x / 6 = 6

cross product

2x = 6 × 6

2x = 36

divide both sides by 2

x = 36 / 2

x = 18

Therefore, the total number of marbles in the bag is 18

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