Question

At Imelda's fruit stand, you bought 5 apples and 4 oranges for $10, and your friend bought 5 apples and 5 oranges for $11. Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?

Answer 1

Apple cost 1.20 and orange 1.00

Explanation:

Answer 2

Let x be price of one apple and y be price of one orange.

Upon using our given information we will get a system of equation as:

`5x+4y=10..(1)`

`5x+5y=11..(2)`

Since we know that a system of equation will have a unique solution if,

`(a_1)/(a_2)\\eq(b_1)/(b_2)`, where
`a_1` and
`b_1` are coefficients of x and y terms of our one equation respectively;
`a_2` and
`b_2` are coefficients of x and y terms of our second equation respectively.

Let us check that our system of equations is solvable or not.

`(5)/(5)\\eq(4)/(5)`

`1\\eq(4)/(5)`

We can see that our system of equation is solvable and will have a unique solution.

We will use substitution method to solve our system of equations.

Upon substituting
`5x=11-5y` in 1st equation we will get,

`11-5y+4y=10`

Upon combining like terms we will get,

`-5y+4y=10-11`

`-y=-1`

Multiplying both sides of our equation by -1 we will get,

`y=1`

Therefore, price of one orange is $1.

Now let us substitute y=1 in 1st equation.

`5x+4\cdot 1=10`

`5x+4=10`

`5x=10-4`

`5x=6`

`x=(6)/(5)`

`x=1.2`

Therefore, price of one apple is $1.2.