The cost of 6 sandwiches and 4 drinks is $53. The code of 4 sandwiches and 6 drinks is $47. How much does one sandwich cost?

$6.50

Step-by-step explanation:

SET UP A SYSTEM OF EQUATIONS WHERE SANDWHICHES IS REPRESENTED BY S AND DRINKS BY D:

6S+4D = 53

4S+6D=47

ADD THEM TOGETHER

10S+10D=100

SOLVE FOR D

10D = 100 - 10S

D = 10-S

SUBSTITUTE THAT VALUE INTO ONE OF THE ORIGINAL EQUATIONS

4S + 6(10-S) = 47

4S + 60 - 6S = 47

COMBINE LIKE TERMS

-2S + 60 = 47

SUBTRACT 60 FROM BOTH SIDES

-2S = -13

DIVIDE BY -2

S = 13/2

S = $6.50

One sandwich is going to cost 6.50 while a drink is going to cost 3.50

Step-by-step explanation:

"We want to find and solve a system of equations to find the cost of one sandwich.

Each sandwich costs $6.50

We can start by defining the variables:

x = price of a sandwich

y = price of a drink.

Then from the given information we can write the equations:

6*x + 4*y = $53

4*x + 6*y = $47

We want to solve this for x, then we need to isolate y in one of the equations. Isolating y in the second equation we get:

y = ($47 - 4*x)/6

Now we can replace this in the other equation and solve it for x:

6*x + 4*($47 - 4*x)/6 = $53

6*x + $31.33 - (16/6)*x = $53

(20/6)*x = $53 - $31.33 = $21.67

x = (6/20)*$21.67 = $6.50" solved by  

facundo3141592

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