Question

An apple farmer sells small and large boxes of apples . In the morning he sells 3 small boxes and 14 large boxes for a total of $203. In the afternoon he sells 11 small boxes and 11 large boxes for a total of $220 . How much money does the farmer sell one small box of apples for ?

Answer 1

The farmer sells one small box of apples for $7.

Explanation:

Suppose, the selling price of one small box is
`x` dollar and one large box is
`y` dollar.

In the morning, the farmer sells 3 small boxes and 14 large boxes for a total of $203. So, the first equation will be......

`3x+14y=203 ...................(1)`

In the afternoon, he sells 11 small boxes and 11 large boxes for a total of $220. So, the second equation will be......

`11x+11y=220 ...................(2)`

Dividing both sides of equation (2), we will get.....

`(11x+11y)/(11)=(220)/(11)\\ \\ \Rightarrow x+y=20\\ \\ \Rightarrow y=20-x`

Now, substituting this
`y= 20-x` into equation (1), we will get.....

`3x+14(20-x)=203\\ \\ 3x+280-14x=203\\ \\ -11x=203-280\\ \\ -11x= -77\\ \\ x=(-77)/(-11)=7`

So, the farmer sells one small box of apples for $7.

Answer 2

The cost of 1 small box of apples = $7.

Explanation:

Let x be the cost of each small box of apples and y be cost of each large box of apples.

We have been given that in the morning he sells 3 small boxes and 14 large boxes for a total of $203. We can represent this information in an equation as:

`3x+14y=203...(1)`

We are also told that in the afternoon he sells 11 small boxes and 11 large boxes for a total of $220. We can represent this information in an equation as:

`11x+11y=220...(2)`

Now we will solve our system of equations using substitution method. From equation (1) we will get,

`y=(203-3x)/(14)`

Upon substituting
`y=(203-3x)/(14)` in equation (2) we will get,

`11x+11((203-3x)/(14))=220`

Upon distributing 11 we will get,

`11x+((2233-33x)/(14))=220`

Now let us have a common denominator on the left hand side of our equation.

`(154x+2233-33x)/(14)=220`

`(121x+2233)/(14)=220`

Upon multiplying both sides both sides on our equation by 14 we will get,

`14*(121x+2233)/(14)=14*220`

`121x+2233=3080`

`121x=3080-2233`

`121x=847`

`x=(847)/(121)=7`

Therefore, the farmer sells each each small box of apples for $7.