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Question

$open parentheses 1 third t plus 5 close parentheses plus open parentheses 1 half u minus 4 close parentheses equals 37$
$open parentheses 1 third t plus 5 close parentheses minus open parentheses 1 half u minus 4 close parentheses equals 19$
For the system of equations above, what is the value of the product $open parentheses 1 third t plus 5 close parentheses open parentheses 1 half u minus 4 close parentheses$ ?

The correct answer is: 252

suppose $1 third t plus 5 equals a text and end text 1 half u minus 4 equals b$
We get the equations as $a plus b equals 37 text and end text a minus b equals 19$
Add both the equations $a plus b plus a minus b equals 37 plus 19 not stretchy rightwards double arrow 2 a equals 56$
We get a = 28 .
Substitute a = 28 in $a plus b equals 37$
$28 plus b equals 37 not stretchy rightwards double arrow b equals 37 minus 28$
We get b = 9
We get $open parentheses 1 third t plus 5 close parentheses cross times open parentheses 1 half u minus 4 close parentheses equals a cross times b equals 28 cross times 9 equals 252.$

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