To determine which option uses intercepts that have viable solutions, let's analyze each option:
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Option #1: (number of quarters, number of dimes) - Both quarters and dimes are types of currency. In this case, the intercepts could represent scenarios where one type of coin is 0 (for example, if there are 0 quarters, there would still be a certain number of dimes). This option has viable solutions as it's practical to have a combination of these coins.
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Option #2: (human age, human weight) - Age cannot be negative and generally has an upper limit, while weight also cannot be negative. However, the relationship between these two variables is not characterized by intercepts in a typical sense (like in linear equations). For example, a person's weight is not defined at an age of 0 (infants have weight, but it changes rapidly). Therefore, it doesn't represent viable intercepts in a meaningful way.
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Option #3: (height, shoe size) - Like age and weight, height and shoe size do relate but do not have clear intercepts that make sense in the real world. A height of 0 and shoe size of 0 do not represent viable human attributes.
Based on this analysis, Option #1: (number of quarters, number of dimes) uses intercepts that have viable solutions.