how much does each type of candy cost

Question

chase and sara went to the candy store. chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $7.50. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. How much does each type of candy cost?

Answer 1

Hi EJ

 

This is what math people call a system of equations.

 

Chase spent $7.50 for 5 FUDGE  and  3 GUM.

 

Sara spent $3.60  for 2 FUDGE and 10 GUM.

 

As equations these would be  (using F for FUDGE and G for GUM)

 

7.50 = 5F + 3G

3.60 = 2F + 10G

 

Now you can solve by substitution (solve the bottom equation for F, and plug your newly found F into the top equation) or by elimination where you would multiply the whole top by -2, and the whole bottom by 5, this would cause the "F" term on top to be -10F  and the "F" term on the bottom to be +10F, and then when you add vertically, the "F"s are eliminated and you are able to find G.

 

By substitution,

F = 1.80-5G,    

Putting this into the top equation gives   

7.50 = 5(1.80-5G) + 3G

And now you can solve for G.  Plug it back in and find F.  These are the prices for Gum and Fudge.

 

By elimination

 

-15.00 = -10F -6G

 18.00 =  10F + 50G

 

Add these vertically and get

 

3.00 = 44 G

 

Solve for G by dividing both sides by 44

 

Plug G back into one of the equations to find F.