Respuesta :
Answer:
The cost of 1 small box of apples = $7.
Step-by-step 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:
[tex]3x+14y=203...(1)[/tex]
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:
[tex]11x+11y=220...(2)[/tex]
Now we will solve our system of equations using substitution method. From equation (1) we will get,
[tex]y=\frac{203-3x}{14}[/tex]
Upon substituting[tex]y=\frac{203-3x}{14}[/tex] in equation (2) we will get,
[tex]11x+11(\frac{203-3x}{14})=220[/tex]
Upon distributing 11 we will get,
[tex]11x+(\frac{2233-33x}{14})=220[/tex]
Now let us have a common denominator on the left hand side of our equation.
[tex]\frac{154x+2233-33x}{14}=220[/tex]
[tex]\frac{121x+2233}{14}=220[/tex]
Upon multiplying both sides both sides on our equation by 14 we will get,
[tex]14*\frac{121x+2233}{14}=14*220[/tex]
[tex]121x+2233=3080[/tex]
[tex]121x=3080-2233[/tex]
[tex]121x=847[/tex]
[tex]x=\frac{847}{121}=7[/tex]
Therefore, the farmer sells each each small box of apples for $7.
Answer:
The farmer sells one small box of apples for $7.
Step-by-step explanation:
Suppose, the selling price of one small box is [tex]x[/tex] dollar and one large box is [tex]y[/tex] 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......
[tex]3x+14y=203 ...................(1)[/tex]
In the afternoon, he sells 11 small boxes and 11 large boxes for a total of $220. So, the second equation will be......
[tex]11x+11y=220 ...................(2)[/tex]
Dividing both sides of equation (2), we will get.....
[tex]\frac{11x+11y}{11}=\frac{220}{11}\\ \\ \Rightarrow x+y=20\\ \\ \Rightarrow y=20-x[/tex]
Now, substituting this [tex]y= 20-x[/tex] into equation (1), we will get.....
[tex]3x+14(20-x)=203\\ \\ 3x+280-14x=203\\ \\ -11x=203-280\\ \\ -11x= -77\\ \\ x=\frac{-77}{-11}=7[/tex]
So, the farmer sells one small box of apples for $7.
