Question

it takes dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. he has been making bracelets for longer than 120 minutes. if ( x ) represents the number of simple bracelets that he has made and ( y ) represents the number of deluxe bracelets he has made, the inequality ( 9x + 20y > 120 ) represents the scenario.

which is a possible combination of bracelets that dimitri may have made?

0 simple bracelets and
6 deluxe bracelets

12 simple bracelets and
0 deluxe bracelets

3 simple bracelets and
4 deluxe bracelets

7 simple bracelets and
3 deluxe bracelets

Explanation:

Step1: Check 0 simple, 6 deluxe

Substitute \(x = 0\), \(y = 6\) into \(9x + 20y\):
\(9(0) + 20(6) = 0 + 120 = 120\). The inequality is \(9x + 20y > 120\), so \(120\) is not greater than \(120\). Reject.

Step2: Check 12 simple, 0 deluxe

Substitute \(x = 12\), \(y = 0\):
\(9(12) + 20(0) = 108 + 0 = 108\). \(108 < 120\), so reject.

Step3: Check 3 simple, 4 deluxe

Substitute \(x = 3\), \(y = 4\):
\(9(3) + 20(4) = 27 + 80 = 107\). \(107 < 120\), reject.

Step4: Check 7 simple, 3 deluxe

Substitute \(x = 7\), \(y = 3\):
\(9(7) + 20(3) = 63 + 60 = 123\). \(123 > 120\), satisfies the inequality.

Answer:

7 simple bracelets and 3 deluxe bracelets