Question

Devi always brings her own shopping bags to buy fruits. A bag with 74 oranges in it has a mass of 3.72 kg. The same bag with 41 oranges in it has a mass of 2.07 kg. Find the mass of the bag when it is empty in grams.

Answer 1

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Answer 2

The mass of the empty bag is 0.02 kg i.e. 20g

The mass of each orange is 0.05kg i.e. 50g.

In the given word problem formulation, we have two unknown masses ( of the fruit and the bag ) i.e. two variables.

Let us assume the mass of each orange is "x" kgs and the mass of the fruit bag is "y" kgs.

Equation 1 :

The mass of the bag with 74 oranges is given to be 3.72 kg. Converting it to an equation :

    Mass of filled bag = Mass of Empty bag + Mass of 74 oranges

                 $3.72 = y + 74x$

Equation 2 :

The mass of the same bag with 41 oranges is given to be 2.07 kg. Converting it to an equation :

    Mass of filled bag = Mass of Empty bag + Mass of 41 oranges

                 $2.07 = y + 41x$

Now, we have two equations and two variables. Let us use the Elimination Method to solve the given system of equations and the value of the associated variables.

Subtracting Equation 2 from Equation 1 :

           $3.72 - 2.07 = (y+74x) - (y+41x)\\1.65 = y - y + 74x - 41x\\1.65 = (74-41)x\\1.65 = 33x\\x = 1.65/33\\x = 0.05kg$

Substituting the value of variable "x" in Equation 1 to get "y" :

         $3.72 = y + 74x\\3.72 = y + 74(0.05)\\3.72 = y + 3.7\\y = 3.72 - 3.70\\y = 0.02kg$

Hence, the mass of the empty bag is 0.02 kg i.e. 20g and the mass of each orange is 0.05kg i.e. 50g.

To learn more about the Elimination method, visit

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