Question

A fruit stand has to decide what to charge for their produce. They need $5.30 for 1 apple and 1 orange. They also need $7.30 for 1 apple and 2 oranges. We put this information into a system of linear equations.

Can we find a unique price for an apple and an orange?

Answer 1

The price of an apple = $ 3.30

The price of an orange = $ 2

Step by step solution:

A fruit stand has to decide what to charge for their produce.

1. They need $ 5.30 for 1 apple and 1 orange.

2. They also need $ 7.30 for 1 apple and 2 oranges.

A. To put this information into a system of linear equations.

B.We need to find a unique price for an apple and an orange.

So we'll use X and Y to find our answer.

Apple = x Orange = y

A. The first condition that they need $ 5.30 for 1 apple and 1 orange we get

- Equation 1 -

To retrace our steps from the second condition they need $7.30 for 1 apple and 2 oranges, that we get.

- Equation 2 -

The required set of Linear Equations are...

1. x + y = 5.30

2. x + 2y = 7.30

Equation 2 & Equation 1

We get...

y = 2

From Equation 1

We get...

x = 5.30 - 2 = 3.30

So when we put it all together...

We get...

1. The price of an apple = $ 3.30

2. The price of an orange = $ 2

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Hope this helps!

Answer 2

A fruit stand has to decide what to charge for their produce.

They need $ 5.30 for 1 apple and 1 orange.

They also need $ 7.30 for 1 apple and 2 oranges.

TO DETERMINE

To put this information into a system of linear equations.

TO find a unique price for an apple and an orange

EVALUATION

Let the price of an apple = x and price of an orange = y

So From the first condition that they need $ 5.30 for 1 apple and 1 orange we get

\sf{x + y = 5.30}x+y=5.30 - - - - Equation 1

Again from second condition that they need $ 7.30 for 1 apple and 2 oranges we get

\sf{x + 2y = 7.30}x+2y=7.30 - - - - Equation 2

So the required Set of linear equations are

x + y = 5.30

x + 2y = 7.30

Equation (2) - Equation (1) we get

y = 2

From Equation (1) we get

x = 5.30 - 2 = 3.30

Hence price of an apple = $ 3.30

The price of an orange = $ 2