A box had twice as many grapes as a basket. after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. how many kilograms of grapes did the basket contain?

Respuesta :

Let us suppose that the number of grapes in the box is x and the number of grapes in the basket is y.

It means that the weight of the grapes in the box is x kg and that of basket is y kg.

It has been given that the box had twice as many grapes as a basket. Therefore, we have

[tex]x=2y[/tex]

Now when we add 2 kg to the basket then the weight of the basket is y+2 and the weight of box will remain same.

Now, we have been given that after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. Hence, we have

[tex]y+2=x+0.5[/tex]

Substituting the value x=2y in the equation, we get

[tex]y+2=2y+0.5\\ -y=-1.5\\ y=1.5[/tex]

Therefore, the basket contains 1.5 kilograms of grapes.

The basket contains the quantity of the grapes is 1.5 kg and the box contains grapes is 3 kg.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

A box had twice as many grapes as a basket.

After 2 kilograms were added to the basket it contained 0.5 kilograms more than the box.

Let y be the grapes in the box and x be the grapes in the basket.

According to the first condition, we have

y = 2x

On simplifying, we have

2x - y = 0 ...1

According to the second condition, we have

x + 2 = y + 0.5

On simplifying, we have

x - y = -1.5 ...2

On solving equations 1 and 2, we have

x = 1.5

y = 3

More about the linear system link is given below.

https://brainly.com/question/20379472

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