Three sandwiches and a hotdog cost $65, while one sandwich and 3 hotdogs $35. How much two sandwiches and 2 hotdogs cost?

Question

I couldn't get the right equation in this word problem. What must be the correct solution?Your best explanation would be a great help. Thanks.

Answer 1

Set up the equations as s (sandwiches); h (hotdogs):

 3s + h = 65

  s + 3h = 35

Use the elimination of 1 variable to solve for the other.

Eliminating h and solving for s:

3s + h = 65
s + 3h = 35 (multiply this by -3)

-------------------------------------

3s + h = 65
-3s - 9h = -105

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    -8h = -40

     h = 5 (hotdogs cost $5 each)

 

Now, substitute h in 1 of the equations to solve for s:

3s + 5 = 65

     -5     -5

---------------

3s       = 60

   s = 20 (sandwiches cost $20 each)

 

Check the 2 equations:

3(20) + 5 ? 65

60 + 5 ? 65

65 = 65 (check)

 

20 + 3(5) ? 35

20 + 15 ? 35

35 = 35 (check)

 

Now, solve for the last one:

2s + 2h = ?

2(20) + 2(5) = ?

40 + 10 = 50 (the cost for 2 hotdogs and 2 sandwiches)

Answer 2

It's best to start by writing an expression for each piece of information given. Assign variables for the unknown quantities.

 

let;

S = cost of a sandwich

H = cost of a hotdog

 

Three sandwiches and a hotdog cost $65,

3S + H = 65

 

while one sandwich and 3 hotdogs $35.

S + 3H = 35

 

Now we have two expressions and two unknown variables. Rewrite an expressions in terms of one variable.

 

S + 3H = 35

S = 35 - 3H

 

Substitute this in for S in the other equation.

 

3S + H = 65

3(35 - 3H) + H = 65

 

105 - 9H + H = 65

105 - 8H = 65

105 - 65 = 8H

40 = 8H

5 = H

 

Now use H to solve for S

 

S + 3(5) = 35

S + 15 = 35

S = 20

Answer 3

3s + h = 65

s + 3h = 35

 

So let's isolate s in equation 2 and then plug it into eq 1.

 

s = 35-3h

 

3(35-3h) + h = 65

105 - 9h + h =65

-8h = -40

h=5

 

s = 35-3(5) = 35-15=20

 

So 2s + 2h = 2(20) + 2(5) = 40+10 =50 (but at those prices stay they heck away from this sandwich shop).