How many ordered pairs of positive integers (x, y) satisfy the equation 5x + 2y = 85?

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Infinite

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Official Explanation

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To find the number of ordered pairs of positive integers (x, y) that satisfy the equation 5x + 2y = 85, we start with the equation: 5x + 2y = 85. Rearranging gives us 2y = 85 - 5x. We need to determine the positive integer values of x for which 85 - 5x is a multiple of 2. The expression 85 - 5x is even when x is odd. Additionally, we…

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What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.