Question

A jar contains sugar.
The jar and the sugar have a total weight of 850 g.
Anna uses of the sugar.
The jar and the sugar now have a total weight of 530 g.
Work out the weight of the jar.

Answer 1

The weight of the jar is 210 g.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here, according to the given information, we are given that,

The jar and the sugar have a total weight of 850 g.

This means that if x and y be the weights of the jar and sugar respectively,

x + y = 850.

Now, we also have that,

$x+\frac{y}{2} =530$

That is, 2x + y = 1060.

Subtracting the first equation from the second equation, we get,

x = 210.

This means, y = 850 - x = 850 - 210 = 640.

Hence, the weight of the jar is 210 g.

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Answer 2

Weight of the jar = 370 grams  

Given:

The jar and the sugar have a total weight of 850 g

Anna used 2/3 of the sugar

The jar and the sugar now have a total weight of 530 g.

To find:

The weight of the jar

Solution:

Complete Question:  

A jar contains sugar. The jar and the sugar have a total weight of 850 g. Anna uses 2/3 of the sugar. The jar and the sugar now have a total weight of 530 g. Work out the weight of the jar.

Let x be the weight of the jar and y be the sugar weight

By the given data,

x + y = 850g ----- (1)

After using 2/3 of the sugar

=> $x + \frac{2}{3} y = 530 g$  

=> $x + \frac{3y - 2y}{3} = 530 g$

=> $x + \frac{y }{3} = 530 g$

=> $3x + y =1590$ ---- (2)

Subtract (1) from (2)

=>  $3x + y - (x + y) = 1590 - 850$

=>  $3x + y - x - y = 740$

=>  $2x = 740$

=> x = 370  

As we assumed the weight of the jar = x g = 370 grams                                          

Therefore,

Weight of the jar = 370 grams  

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