fond the cost of each item

Question

A customer buys 5 hot dogs and 5 bags of potatoe chips for 12.50. Another customer buys 3 hot dogs and 4 bags of potatoe chips for 8.25.find the cost of each item.

Answer 1

Let h = the cost of a hot dog and c = the cost of a bag of chips.

• customer buys 5 hot dogs and 5 bags of potato chips for 12.50:  5h + 5c = $12.50
• Another customer buys 3 hot dogs and 4 bags of chips for 8.25: 3h + 4c = $8.25

 

Let's eliminate the h variable by making their coefficients equal but opposite in sign:

 

-3*(5h + 5c = 12.50) = -15h - 15c = -37.50

5*(3h + 4c = 8.25) =     15h + 20c = 41.25

                                  

Now add the equations together:

 

-15h - 15c = -37.50
 15h + 20c = 41.25
-------------------------
   0   + 5c  = $3.75

 

5c = $3.75

c = $0.75

 

To find h, plug c = $0.75 into either original equation and solve for h:

 

3h + 4c = 8.25

3h + 4($0.75) = $8.25

3h + $3.00 = $8.25

3h = $5.25

h = $1.75

 

Check your answers by plugging them back into the original equations:

 

5h + 5c = 12.50

5($1.75) + 3($0.75) = $12.50

$8.75 + $3.75 = $12.50

$12.50 = $12.50    CHECK!

 

3h + 4c = 8.25

3($1.75) + 4($0.75) = $8.25

$5.25 + $3.00 = $8.25

$8.25 = $8.25       CHECK!