Question

A fruit stand has to decide what to charge for their produce. They need $5 for 1 apple and 1 orange. They also need $15 for 3 apples and 3 oranges. Put this information into a system of linear equations. find a unique price for an apple and an orange?

Answer 1

The system has many solutions. The unique price for an apple and an orange cannot be found

Solution:

Let the cost of each apple be x

Let the cost of each orange be y

They need $5 for 1 apple and 1 orange

Therefore,

x + y = 5 ----- eqn 1

They also need $15 for 3 apples and 3 oranges

Therefore,

3x + 3y = 15 -------- eqn 2

Solve eqn 1 and eqn 2

Multiply eqn 1 by 3

3x + 3y = 15 ------- eqn 3

Subtract eqn 2 from eqn 3

3x + 3y = 15

3x + 3y = 15

( - )  -----------------

0 = 0

Thus the system of equations has many solutions

Infinite solutions would mean that any value for the variable would make the equation true

Learn more about this topic

Show that the system of equations 2x+5y=17 , 5x+3y=14 has a unique solution find the solution

https://brainly.in/question/3956399

3 oranges & 2apples. Cost 22. If price of orange increase by 25% & that of apple inceease by 20% then 2 oranges & 3 apples cost 28. Find out the actual price of an apple

https://brainly.in/question/1605681