[tex]\bold{\huge{\blue{\underline{Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
- Customer 1 bought 2 hamburgers and 4 drinks at a cost of $13.00
- Customer 2 bought 3 hamburgers and 7 drinks at a cost of $21.00
[tex]\bold{\underline{ To \: Find :- }}[/tex]
- We have to find the total cost of 8 drinks and 9 hamburgers
[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
Let the cost of hamburgers and drinks be x and y
According to the question,
[tex]\sf{ 2x + 4y = 13.00 ...eq( 1 ) }[/tex]
[tex]\sf{ 3x + 7y = 21.00 ...eq(2) }[/tex]
Solving eq( 1 ) we get :-
[tex]\sf{ 2x + 4y = 13 }[/tex]
[tex]\sf{ 2x = 13 - 4y }[/tex]
[tex]\sf{ x = (13 - 4y)/2 ...eq(3)}[/tex]
Subsituting eq(3) in eq( 2 ) :-
[tex]\sf{ 3( 13 - 4y)/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y + 14y = 42}[/tex]
[tex]\sf{ 2y = 42 - 39 }[/tex]
[tex]\sf{ 2y = 3 }[/tex]
[tex]\sf{ y = 3/2 }[/tex]
Subsituting value of y in eq(3) :-
[tex]\sf{ x = 13 - 4(3/2)/2}[/tex]
[tex]\sf{ x = 13 - 2(3)/2}[/tex]
[tex]\sf{ x = 13 - 6/2}[/tex]
[tex]\sf{ x = 7/2 }[/tex]
Therefore,
[tex]\sf{ Cost\: of \:8 \:drinks}[/tex]
[tex]\sf{ = 8 * 3/2 }[/tex]
[tex]\sf{ = 4 * 3 }[/tex]
[tex]\sf{ = 12.00 dollars}[/tex]
And
[tex]\sf{ Cost\: of \:9 \:hamburgers }[/tex]
[tex]\sf{ = 9 * 7/2 }[/tex]
[tex]\sf{ = 63/2}[/tex]
[tex]\sf{ = 31.50 dollars}[/tex]
Total cost of the 8 drinks and 9 hamburgers
[tex]\sf{ 12.00 + 31.50}[/tex]
[tex]\sf{\red { = 43.50 \:dollars}}[/tex]
Hence, The total cost paid by you for 8 drinks and 9 hamburgers is $43.50 .
