Question

Mr. Jones purchased two sodas.

The total cost was $1.10. One soda
was exactly one dollar more than
the other soda. What was the
price of each soda separately? *

Answer 1

the prices were $0.05 and $1.05

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

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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.

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Additional comment

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, the larger value is half the sum of the sum and difference: a = (1+1.10)/2 = 1.05. If we were to subtract one equation from the other, we would find the smaller value is half the difference of the sum and difference: b = (1.05 -1.00)/2 = 0.05.

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