Counts and Prices

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A fishing boat receives $1.50 for each tuna it brings back to port and $1.80 for each mackerel. How many mackerels did it bring back to port yesterday?

(1) Yesterday the number of tuna that the boat brought back was 5 less than twice the number of mackerel brought back.

(2) Yesterday the boat received a total of $2,960 from tuna and mackerel brought back.

Review: Counts and Prices




Explanation

We look at this question and we see algebra. This is a classic word problem in which algebraic statements have been expressed in English. Most likely, we will use the n variables, n equations here. I.e., we are missing the number of mackerels and the number of tuna. If we can form two distinct equations with those variables, we'll be able to solve for both variables. On to the statements, which we'll look at separately. The first statement gives



Which is a good equation, but we only have one total. So the first statement is insufficient. The second statement gives me



Which logically has the same problem--we have only one equation, total. However, if we combine the statements, we have two equations for two variables, so the n variables, n equations rule is satisfied, and we'll be able to solve for both T and M. So the statements are sufficient together. In practice this can all be done without writing the equations, so long as you are certain that the equations are distinct and they are linear equations.

The correct answer is (C).


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