Question

A multimeter and an oscilloscope cost $574. The oscilloscope cost $356 more than the multimeter. Find the cost of the oscilloscope and the multimeter.

Answer 1

• oscilloscope: $465
• multimeter: $109

Explanation:

You want the costs of an oscilloscope and a multimeter when the sum of their costs is $574, and the difference of their costs is $356.

Sum and difference

Let o and m represent the costs of the oscilloscope and multimeter, respectively. Then the costs can be described by ...

o +m = 574

o -m = 356

Solution

Adding these two equations gives ...

2o = (574+356) = 930

o = 465 . . . . . . . . . . . . divide by 2

Subtracting the second equation from the first gives ...

2m = 574 -356 = 218

m = 109 . . . . . . . . . . . . divide by 2

The oscilloscope costs $465; the multimeter costs $109.

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Additional comment

This is the generic solution to a "sum and difference" problem: the higher value is half the sum of the given numbers, and the lower value is half their difference.