Question

Ed decides to include more fruit in his diet. He goes to the grocery store over the weekend and buys 6 apples, 6 oranges, and 6 avocados. The total cost is $19.50.

Ed finishes the apples very quickly, and has some leftover avocado. The following weekend he buys 12 apples, 2 oranges, and 1 avocado. This time he pays just $9.50.

The following week, Ed reads an article on the benefits of avocado, so over the weekend he buys 5 avocados along with 2 apples and 4 oranges. His total this time is $14.

Assume that Ed pays a unit price rather than a price per pound for the apples, oranges, and avocados.

Answer 1

9514 1404 393

Answer:

• apples: $0.50 ea
• oranges: $0.75 ea
• avocados: $2.00 ea

Explanation:

Let a, o, v represent the prices of one each of apples, oranges, and avocados, respectively. Then the equations describing the purchases can be written ...

6a +6o +6v = 19.50

12a +2o +1v = 9.50

2a +4o +5v = 14.00

__

Dividing the first equation by 6 makes it ...

a +o +v = 3.25

Subtracting this from the second equation gives ...

(12a +2o +v) -(a +o +v) = (9.50) -(3.25)

11a +o = 6.25

Subtracting the third equation from 5 times the reduced first equation gives ...

5(a +o +v) -(2a +4o +5v) = 5(3.25) -(14.00)

3a +o = 2.25

The difference of these last two equations is ...

(11a +o) -(3a +o) = (6.25) -(2.25)

8a = 4.00

a = 0.50

Then the other values are ...

o = 2.25 -3(a) = 0.75

v = 3.25 -a -o = 2.00

The unit prices are:

apples -- $0.50

oranges -- $0.75

avocados -- $2.00

_____

Additional comment

Most graphing or scientific calculators will solve systems of equations like these. Using an appropriate tool, it takes less time to find the solution than to read this one.

Note that the last purchase description in the problem statement has the items in a different order than in the first two descriptions. Care must be taken to make sure the correct equations are written.