Algebra 1 math for quiz

Question

A fruit stand has to decide what to charge for their produce. They need $10, 4 apples and 4 oranges. They also need $15 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

4A + 4O = 10

6A +6O = 15

are two equations that are linearly dependent with an infinite number of solutions. There is no unique solution

Price of apples = A, Price of Oranges = 0

A O

$.01 $2.49

$.02 $2.48

$.03 $2.47

$.25 $2.25

$.50 $2

$.75 $1.75

$1 $1.50

$1.25 $1.25

$1.50 $1

$1.75 75 cents

$2 50 cents

$2.25 25 cents

$2.48 2 pennies

$2.49 1 penny

are just 14 of 249 solutions where the price of apples and oranges have prices that are cents that are integers. Theoretically, there's an infinite number of prices, but that include fractional penny prices which are not realistic. Make it 251 if you include a free apple and an orange for $2.50 or vice versa

the price of apples plus the price of oranges = $2.50

4A + 4O = $10

divide by 4

A + O = $10/4 = $2.50

same with the 2nd equation

6A + 6O = $15

divide by 6

A + O = 15/6 = $2.50