Question

A fruit stand has to decide what to charge for their produce. They need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 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

Given:

The price of 111 apples and 111 oranges = $5.30

The price of 111 apples and 222 oranges = $7.30

To find:

The price of an apple and an orange

Solution:

The above given question is a problem on linear equations.

Let's assume "a" be the price of an apple and "o" be the price of an orange.

According to the question, we get two of the linear equations as,

111 a + 111 o = 5.30 ..... (i)

and

111 a + 222 o = 7.30 ........ (ii)

Now, we will subtract (i) from (ii), we get

111 a + 222 o = 7.30

111 a + 111 o = 5.30

-       -            -

-----------------------------------

        111 o = 2

---------------------------------------

∴ o = $\frac{2}{111}$ = $0.0180 ← price of an orange

Substituting the value of o in equation (i), we get

111 a + [111 × $\frac{2}{111}$] = 5.30

⇒ 111 a + 2 = 5.30

⇒ 111 a = 5.30 - 2

⇒ 111 a = 3.3

⇒ a = $0.0297 ← price of an apple

Thus, $\boxed{\bold{The\: unique\: price\:for \:an \:apple\: is\:\ \:0.0297 \:and \:an\:orange\: \ \:0.0180.}}$

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Answer 2

Given :   need $5.30 for 1 apple and 1  orange .  need $7.30 for 1 apple and 2  orange .

To find : a unique price for an apple and an orange

Solution:

Apple price =  A  $

Orange price = B  $

$5.30 for 1 apple and 1  orange

=> A + B  = 5.30    Eq1

$7.30 for 1 apple and 2  orange .

=> A  + 2B = 7.30   Eq2

Eq2 - Eq1

=> B = 2

Price of Orange = 2$

A + 2 = 5.30

=> A= 3.30 $

Price of Apple  = 3.3 $

Price of Apple  = 3.3 $

Price of Orange = 2$

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