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39 packs of coffee were sold at a coffee shop, and 45 packs of tea, for which the costumers payed 738. The next day 11 packs of coffee were sold and 13 packs of tea, which made 210 dollars. How much does each package cost

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The cost of one pack of coffee is $12 and cost of one tea pack is $6.

Step-by-step explanation:

Let,

Cost of one pack of coffee = x

Cost of one pack of tea = y

According to given statement;

39x+45y=738    Eqn 1

11x+13y=210       Eqn 2

Multiplying Eqn 1 by 11

[tex]11(39x+45y=738)\\429x+495y=8118\ \ \ Eqn\ 3\\[/tex]

Multiplying Eqb 2 by 39

[tex]39(11x+13y=210)\\429x+507y=8190\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 3 from Eqn 4

[tex](429x+507y)-(429x+495y)=8190-8118\\429x+507y-429x-495y=72\\12y=72[/tex]

Dividing both sides by 12

[tex]\frac{12y}{12}=\frac{72}{12}\\y=6[/tex]

Putting y=6 in Eqn 2

[tex]11x+13(6)=210\\11x+78=210\\11x=210-78\\11x=132[/tex]

Dividing both sides by 11

[tex]\frac{11x}{11}=\frac{132}{11}\\x=12[/tex]

The cost of one pack of coffee is $12 and cost of one tea pack is $6.

Keywords: linear equation, subtraction

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Answer:

A pack of coffee=$12

A pack of tea=$6

Step-by-step explanation:

Let the cost of 1 pack of coffee =c

and the cost of 1 pack of tea =t

we can the write the following equations

39c+45t=738...........eqn(1)

11c+13t=738...........eqn(2)

Multiply eqn(1) by 11

429c+495t=8118...........eqn(3)

Multiply eqn(2) by 39

429c+507t=8190...........eqn(4)

eqn(4)-eqn(3)

This implies

12t=72

Dividing through by 12 ,we get

t=6

substituting the value of t into equation two,we obtain

11c+13(6)=210

11c+78=210

11c=210-78

11c=132

Dividing through by 11,we obtain

c=12