9514 1404 393
Answer:
- apples: $0.50 ea
- oranges: $0.75 ea
- avocados: $2.00 ea
Step-by-step 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
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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
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<em>Additional comment</em>
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.
