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? 3 simple bracelets and 4 deluxe bracelets 0 simple bracelets and 6 deluxe bracelets 12 simple bracelets and 0 deluxe bracelets 7 simple bracelets and 3 deluxe bracelets

Answer 1

Given : 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.

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.

To Find :

Which is a possible combination of bracelets that Dimitri may have made?

3 simple bracelets and 4 deluxe bracelets

0 simple bracelets and 6 deluxe bracelets

12 simple bracelets and 0 deluxe bracelets

7 simple bracelets and 3 deluxe bracelets

Solution:

9x + 20y > 120

3 simple bracelets and 4 deluxe bracelets

x = 3 , y = 4

=> 9x + 20y  = 9(3) + 20(4)  = 107   < 120 hence does not satisfy

0 simple bracelets and 6 deluxe bracelets

x = 0 , y = 6

=> 9x + 20y  = 9(0) + 20(0)  = 120   =  120 hence does not satisfy

12 simple bracelets and 0 deluxe bracelets

x = 12 , y = 0

=> 9x + 20y  = 9(12) + 20(0)  = 108   < 120 hence does not satisfy

7 simple bracelets and 3 deluxe bracelets

x = 7, y = 3

=> 9x + 20y  = 9(7) + 20(3)  = 123   >  120 hence satisfy

7 simple bracelets and 3 deluxe bracelets Satisfy

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Answer 2

$\mathfrak\green{☞Solution}$

9x + 20y > 120

3 simple bracelets and 4 deluxe bracelets.

x = 3,y = 4

=>9x + 20y = 9(3) + 20(4) = 107 <120

$\mathtt\red{Hence, \: Does \: not \: satisfy}$

0 simple bracelets 6 deluxe bracelets

x = 3,y = 4

=>9x + 20y = 9(3) + 20(4) = 107 < 120

$\mathtt\red{Hence, \: Does \: not \: satisfy}$

12 simple bracelets and 0 deluxe bracelets

x = 12,y = 0

=>9x + 20y = 9(12) + 20(0) = 108 < 120

$\mathtt\red{Hence, \: Does \: not \: satisfy}$

7 simple bracelets and 3 deluxe bracelets

x = 7,y = 3

=>9x + 20y = 9(7) + 20(3) = 123 > 120

$\mathtt\green{Hence, satisfy!}$

7 simple bracelets and 3 deluxe bracelets satisfy!