Harga 2 kg mangga, 1 kg jeruk, dan  anggur adalah Rp48.000,00 dan harga  mangga,  jeruk, dan  anggur adalah Rp72.000,00. Harga  mangga, 3 kg jeruk, dan 4 kg anggur Rp124.000,00. Jika Arya membeli  jeruk menggunakan selembar uang Rp50.000,00 maka kembalian yang diperoleh adalah ….

Harga  mangga,  jeruk, dan  anggur adalah Rp48.000,00 dan harga  mangga,  jeruk, dan  anggur adalah Rp72.000,00. Harga  mangga,  jeruk, dan  anggur Rp124.000,00. Jika Arya membeli  jeruk menggunakan selembar uang Rp50.000,00 maka kembalian yang diperoleh adalah ….

Jawab:

Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell harga space 1 space kg space mangga end cell row y equals cell harga space 1 space kg space jeruk end cell row z equals cell harga space 1 space kg space anggur end cell end table

Maka, model matematika sistem persamaan linear tiga variabel (SPLTV) dari masalah di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus y plus z end cell equals cell Rp space 48.000 comma 00 space... space left parenthesis 1 right parenthesis end cell row cell x plus 2 y plus 2 z end cell equals cell Rp space 72.000 comma 00 space... space left parenthesis 2 right parenthesis end cell row cell x plus 3 y plus 4 z end cell equals cell Rp space 124.000 comma 00 space... space left parenthesis 3 right parenthesis end cell end table

Eliminasi persamaan (1) dan (2):

x plus 2 y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 72.000 comma 00 space open vertical bar cross times 2 close vertical bar space space 2 x plus y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 48.000 comma 00 space open vertical bar cross times 1 close vertical bar  2 x plus 4 y plus 4 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 144.000 comma 00 space space space space bottom enclose 2 x plus y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 48.000 comma 00 space minus end enclose space space space space space space space space 3 y plus 3 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 96.000 comma 00 space space space space space space space space space space space space y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 32.000 comma 00 space... space left parenthesis 4 right parenthesis

Eliminasi persamaan (2) dan (3):

x plus 3 y plus 4 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 124.000 comma 00 bottom enclose x plus 2 y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 72.000 comma 00 space minus end enclose space space space space space space space space y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 52.000 comma 00 space... space left parenthesis 5 right parenthesis

Eliminasi persamaan (4) dan (5):

space space y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 32.000 comma 00 space open vertical bar cross times 2 close vertical bar y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 52.000 comma 00 space open vertical bar cross times 1 close vertical bar  2 y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 64.000 comma 00 space space bottom enclose y plus 2 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 52.000 comma 00 space minus end enclose space space space space space space space space space space y equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 12.000 comma 00

Harga 2 space kg jeruk adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 y end cell equals cell 2 cross times Rp space 12.000 comma 00 end cell row blank equals cell Rp space 24.000 comma 00 end cell end table

Maka, uang kembaliannya adalah:

table attributes columnalign right center left columnspacing 0px end attributes row Kembalian equals cell Rp space 50.000 comma 00 minus Rp space 24.000 comma 00 end cell row blank equals cell Rp space 26.000 comma 00 end cell end table

Jadi, kembalian yang diperoleh Arya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 26 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 000 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 00 end table.

 

Dijawab Oleh : Kunjaw