Question

A fruit stand has to decide what to charge for their produce. They need \$10$10dollar sign, 10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 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

no

Explanation:

The prices are inconsistent, so there is no unique price that can be set for either an apple or an orange that will give the total prices indicated.

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The first relation can be written as ...

$10 = 4A +4O

$10 = 4(A +O) . . . . factor out 4

$2.50 = A +O . . . . divide by 4

The second relation can be written as ...

$12 = 6A +6O

$12 = 6(A +O) . . . . factor out 6

$2 = A +O . . . . . . . divide by 6

These two relations give different prices for 1 apple and 1 orange. There is no price that can be set for either fruit that will give this result.

No unique prices can be assigned.