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Linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

Tony spends $80 per month on public transportation. A 10-ride pass costs $12.50, and a single-ride pass costs $1.50. If g represents the number of 10-ride passes Tony buys in a month and t represents the number of single-ride passes Tony buys in a month, which of the following equations best represents the relationship between g and t ?

ExplanationShow

Choice D is correct. Since a 10-ride pass costs $12.50 and g is the number of 10-ride passes Tony buys in a month, the expression $12 point 5 0 g$ represents the amount Tony spends on 10-ride passes in a month. Since a single-ride pass costs $1.50 and t is the number of single-ride passes Tony buys in a month, the expression $1 point 5 0 t$ represents the amount Tony spends on single-ride passes in a month. Therefore, the sum $12 point 5 0 g, plus 1 point 5 0 t$ represents the amount he spends on the two types of passes in a month. Since Tony spends a total of $80 on passes in a month, this expression can be set equal to 80, producing $12 point 5 0 g, plus 1 point 5 0 t, equals 80$ .

Choices A and B are incorrect. The expression $g plus t$ represents the total number of the two types of passes Tony buys in a month, not the amount Tony spends, which is equal to 80, nor the cost of one of each pass, which is equal to $1 point 5 0, plus 12 point 5 0$ . Choice C is incorrect and may result from reversing the cost for each type of pass Tony buys in a month.

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Linear equations in two variables SAT question

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