Question

Billy got 180 apples from the orchard. He has 10 boxes that can hold either 10 or 20 apples. Using all the 10 boxes, how many of each kind of box does he need to pack all the apples?​

Answer 1

Let $x$ be the number of boxes which can hold 10 apples.

Let $y$ be the number of boxes which can hold 20 apples.

As per the question, there are a total of 10 boxes.

$x + y = 10 ....... (1)$

Also, there are a total of 180 apples.

If $x$ is the type of box which can contain 10 apples, then total apples in this type of box = $10 \times x$.

And, if $y$ is the type of box which can contain 20 apples, then total apples in this type of box = $20 \times y$.

As per question, there are total 180 apples available.

$\Rightarrow 10x + 20y = 180 ........ (2)$

Using elimination method in equation (1) and equation (2):

$equation (2) - 10 \times equation (2) :\\\Rightarrow 10y = 80\\\Rightarrow y = 8$

Putting value of $y$ in equation (1):

$\Rightarrow x = 10 -8\\\Rightarrow x =2$

So, Billy should have 2 boxes which can hold 10 apples each and

8 boxes which can hold 20 apples each to pack all the 180 apples.

Answer 2

Step-by-step explanation:

Let xx be the number of boxes which can hold 10 apples.

Let yy be the number of boxes which can hold 20 apples.

As per the question, there are a total of 10 boxes.

x + y = 10 ....... (1)x+y=10.......(1)

Also, there are a total of 180 apples.

If xx is the type of box which can contain 10 apples, then total apples in this type of box = 10 \times x10×x .

And, if yy is the type of box which can contain 20 apples, then total apples in this type of box = 20 \times y20×y .

As per question, there are total 180 apples available.

\Rightarrow 10x + 20y = 180 ........ (2)⇒10x+20y=180........(2)

Using elimination method in equation (1) and equation

⇒10y=80

⇒y=8