Jane wishes to buy bubble gum and candy bars. Bubble gum costs $1.00 and candy bars cost $1.50. She has $12.00 to spend and wants to buy 8 items.

Question

Write equations for this situation and solve the system of equations. Define your variables

Answer 1

Greetings fellow FLoridian

 

X = # of candy bars

Y = bubble gum

 

X + Y = 8

 

 150X + 100Y  = 1200  <-- written in pennies

 

Solving the first equation for the bubble gum, Y = 1200 - 150 X

Substituting this into the second equation:

 

150X + 100( 1200 - 150 X) = 1200

150X + 120000 - 15000X) = 1200   <-- distributive

 

0 = 1200 - 120000 + 15000X - 150X <--- moves everything to right side; signs change

 

0 = 14850X - 118800

 

X = 118800/14850 = 8

 

So she can buy 8 candy bars. At $1.50 each, the total cost is exactly $12. (no sales tax specified)

 

In exchange for one of the candy bars, she can by the bubble gum.

7 candy bars at $1.50 each is $10.50 plus the bubble gum makes it $11.50. She will get 50 cents change.

 

She could exchange 2 candy bars for bubble gum and get change back.

Likewise she could exchange 3,4,5... candy bars for bubble gum.

Note that 3 bubbles gums can be exchanged for 2 cars bars, and vice versa

 

The following table summarizes

these purchases:

 

 # Candy Bars # Bubble Gum Price Candy Bar Price Bubble Gum    TOTAL        Change
          8                 0                     $12.00               $-                  $12.00           $-
          7                 1                     $10.50              $1.00              $11.50           $0.50
          6                 2                     $9.00                $2.00              $11.00           $1.00
          5                 3                     $7.50                $3.00              $10.50           $1.50
          4                 4                     $6.00                $4.00               $10.00          $2.00
          3                 5                     $4.50                $5.00                $9.50           $2.50
          2                 6                    $3.00                 $6.00                $9.00           $3.00
          1                 7                    $1.50                 $7.00                $8.50           $3.50
          0                 8                    $-                      $8.00                 $8.00          $4.00