Question

The table shows the purchases of two customers at a concession stand at the basketball game. Hamburgers Drinks Total Cost Customer 1 2 $13.00 Customer 2 3 7 $21.00 You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?​

Answer 1

`\bold{\huge{\blue{\underline{Solution}}}}`

`\bold{\underline{ Given :- }}`

• 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

`\bold{\underline{ To \: Find :- }}`

• We have to find the total cost of 8 drinks and 9 hamburgers

`\bold{\underline{ Let's \: Begin :- }}`

Let the cost of hamburgers and drinks be x and y

According to the question,

`\sf{ 2x + 4y = 13.00 ...eq( 1 ) }`

`\sf{ 3x + 7y = 21.00 ...eq(2) }`

Solving eq( 1 ) we get :-

`\sf{ 2x + 4y = 13 }`

`\sf{ 2x = 13 - 4y }`

`\sf{ x = (13 - 4y)/2 ...eq(3)}`

Subsituting eq(3) in eq( 2 ) :-

`\sf{ 3( 13 - 4y)/2 + 7y = 21 }`

`\sf{ 39 - 12y/2 + 7y = 21 }`

`\sf{ 39 - 12y + 14y = 42}`

`\sf{ 2y = 42 - 39 }`

`\sf{ 2y = 3 }`

`\sf{ y = 3/2 }`

Subsituting value of y in eq(3) :-

`\sf{ x = 13 - 4(3/2)/2}`

`\sf{ x = 13 - 2(3)/2}`

`\sf{ x = 13 - 6/2}`

`\sf{ x = 7/2 }`

Therefore,

`\sf{ Cost\: of \:8 \:drinks}`

`\sf{ = 8 * 3/2 }`

`\sf{ = 4 * 3 }`

`\sf{ = 12.00 dollars}`

And

`\sf{ Cost\: of \:9 \:hamburgers }`

`\sf{ = 9 * 7/2 }`

`\sf{ = 63/2}`

`\sf{ = 31.50 dollars}`

Total cost of the 8 drinks and 9 hamburgers

`\sf{ 12.00 + 31.50}`

`\sf{\red { = 43.50 \:dollars}}`

Hence, The total cost paid by you for 8 drinks and 9 hamburgers is $43.50 .