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Mathematics , 17.02.2022 17:53

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?

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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,

\frac{a_1}{a_2}\neq\frac{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.

\frac{5}{5}\neq\frac{4}{5}

1\neq\frac{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=\frac{6}{5}

x=1.2

Therefore, price of one apple is $1.2.  

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Apple cost 1.20 and orange 1.00

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