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Shtirlitz [24]
2 years ago
6

Mr. Jones purchased two sodas.

Mathematics
1 answer:
kondaur [170]2 years ago
5 0

Answer:

  the prices were $0.05 and $1.05

Step-by-step explanation:

Let 'a' and 'b' represent the costs of the two sodas. The given relations are ...

  a + b = 1.10 . . . . the total cost of the sodas was $1.10

  a - b = 1.00 . . . . one soda costs $1.00 more than the other one

__

Adding these two equations, we get ...

  2a = 2.10

  a = 1.05 . . . . . divide by 2

  1.05 -b = 1.00 . . . . . substitute for a in the second equation

  1.05 -1.00 = b = 0.05 . . . add b-1 to both sides

The prices of the two sodas were $0.05 and $1.05.

_____

<em>Additional comment</em>

This is a "sum and difference" problem, in which you are given the sum and the difference of two values. As we have seen here, <em>the larger value is half the sum of the sum and difference</em>: a = (1+1.10)/2 = 1.05. If we were to subtract one equation from the other, we would find <em>the smaller value is half the difference of the sum and difference</em>: b = (1.05 -1.00)/2 = 0.05.

This result is the general solution to sum and difference problems.

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