SOLUTION: Sally went to the market to buy some fruit. She wanted to buy apples, strawberries, and oranges. If she buys two apples, 3 quarts of strawberries and 4 oranges, the fruit would c

Question 1159143: Sally went to the market to buy some fruit. She wanted to buy apples, strawberries, and oranges. If she buys two apples, 3 quarts of strawberries and 4 oranges, the fruit would cost $15.30. If she buys 1 quart of strawberries, 4 apples, and 2 oranges, the fruit would cost $10.90. If she buys only one orange, 5 apples and 2 quarts of strawberries, the fruit would cost $13.70. What is the price of each type of fruit?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

a = number of apples
s = number of quarts of strawberries
o = number of oranges

The given information gives us three equations in three unknowns:

There are numerous different methods for solving a system of 3 equations in 3 unknowns; and in many of those methods there are numerous different paths to the solution.

Probably the most elementary is elimination.

Combine the equations in such a way that one unknown is eliminated, resulting in a system of two equations in two unknowns. Then use elimination again to solve for one unknown.

I will only get you started on the path I think I would use by looking at the three equations.

I would use the coefficients of variable o to eliminate that variable.

Multiplying the 3rd equation by 2 and subtracting the 3nd equation yields

Multiplying the 3rd equation by 4 and subtracting the 1st equation yields

Now eliminate one of the two remaining variables in a similar way; solve for the remaining variable; and "work backwards" through your equations to find the values of the other variables.

And of course -- especially if you are a beginner at working problems like this -- check to see that your answers satisfy the original equations.

NOTE: I arbitrarily chose to eliminate o first. That was because the term "1o" in the 3rd equation makes it easy to eliminate variable o.

I could just as well have chosen to eliminate variable s, using the "1s" term in the second equation.

The coefficients 2, 4, and 5 on variable a in the three equations suggest that eliminating variable a first would be more work.

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