A fishing boat receives $1.50 for each tuna it brings back to port and $1.70 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 $2,930 from tuna and mackerel brought back.
Given:Price for each tuna = $1.5
Price for each mackerel = $1.7
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: Yesterday the number of tuna that the boat brought back was 5 less than twice the number of mackerel brought back.
Let the number of tuna brought back be 't' and the number of mackerel brought back be 'm'
t = 2m-5
However, we cannot uniquely determine the value of m, as it can have multiple values possible.
Thus, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Yesterday the boat received a total of $2,930 from tuna and mackerel brought back.
As the price for each tuna is $1.5, and the price for each mackerel is $1.7, 1.5t + 1.7m = 2930
However, we still cannot uniquely determine the value of m using this statement alone. Hence, Statement 2 is insufficient alone as well.
Now, let's look at the combination of Statements 1 and 2:
1.5t + 1.7m = 2930
t = 2m-5
1.5(2m-5) + 1.7m = 2930
Thus, 3m-7.5+1.7m = 2930 => 4.7m = 2937.5
So, m = 625 (Answer)
Hence, the correct answer is
Option C - Both statements together are sufficient, but neither alone is.Hope this helps!