A shipping company uses the box shown.
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Both boys get 14 problems <em>correct </em>of the <em>entire</em> test composed by 120 problems.
<h3>Procedure - Determination of the number of problems that Andy and Bob got correct in a test</h3>In this question we must determine how many questions Andy and Bob got correct. The total of problems () is the sum of problems that neither got correct (
), problems that only Andy got correct (
) and problems that both boys got correct (
). Hence, we have the following algebraic expression:
(1)
And according to the statement, the relationships between the number of problems got correct by Andy and the number of problems that Bob got correct () is described by the following expressions:
(2)
(3)
If we know that and
, then the solution to this system of linear equations is:
(1)
(2)
(3)
The solution of this system is: ,
,
.
Since the quantity of <em>solved</em> problems must be integers, we have the following approximate solution:
Hence, we conclude that both boys get 14 problems <em>correct </em>of the <em>entire</em> test composed by 120 problems.
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