What combination of 3 snacks can i get with $5.00

Question

Small popcorn is 2.75, medium popcorn is 2.99, large popcorn is 3.49, cookie 2.25, lemonade 1.19, candy bar 1.29, granola bar 0.89

Answer 1

I assume you mean that you want 3 different items in each selection (no lemonade, lemonade, lemonade choices).

Let each choice be represented as A, B, C, D, E, F, G

(A = small popcorn, B = medium popcorn, etc)

The possible choices are (starting with "A")

ABC

ABD

ABE

ABF

ABG

ACD

ACE

ACF

ACG

ADE

ADF

ADG

AEF

AEG

AFG

BCD

BCE

BCF

BCG

BDE

BDF

BDG

BEF

BEG

BFG

CDE

CDF

CDG

CEF

CEG

CFG

DEF

DEG

DFG

EFG

Notice that if I select a medium popcorn, there are no choices that add to less than $5 (medium popcorn plus the cheapest other two items - lemonade and granola - add to $5.07) so the only successes will be choices involving items that cost less than $2.99. That means we can cross out all the possibilities that have B and C in them. That reduces our possibilities to:

ADE

ADF

ADG

AEF

AEG

AFG

DEF

DEG

DFE

EFG

Now, just add up the prices on each:

ADE = Small popcorn, cookie, lemonade = $6.19

ADF = Small popcorn, cookie, candy bar = $6.29

ADG = Small popcorn, cookie, granola bar = $5.89

AEF = Small popcorn, lemonade, candy bar = $5.23

AEG = Small popcorn, lemonade, granola bar = $4.83

AFG = Small popcorn, candy bar, granola bar = $4.93

DEF = Cookie, lemonade, candy bar = $4.73

DEG = Cookie, lemonade, granola bar = $4.33

DFG = Cookie, candy bar, granola bar = $4.43

EFG = Lemonade, candy bar, granola bar = $3.37

So the only ones that are less than $5 are:

AEG = Small popcorn, lemonade, granola bar = $4.83

AFG = Small popcorn, candy bar, granola bar = $4.93

DEF = Cookie, lemonade, candy bar = $4.73

DEG = Cookie, lemonade, granola bar = $4.33

DFG = Cookie, candy bar, granola bar = $4.43

EFG = Lemonade, candy bar, granola bar = $3.37

Answer 2

Hi Terri,

Let's approach this logically. Start with the popcorn. You will not be able to buy more than one popcorn of any size because all will exceed your $5 budget. Now, let's talk about the small popcorn:

Small Popcorn: $2.75

Cookie: $2.25

Total: $5.00; no good since only two snacks; no popcorn + cookie combos will work

Small Popcorn: $2.75

Lemonade: $1.19

Candy Bar: $1.29

Total: $5.23; no good, over budget

Small Popcorn: $2.75

Lemonade: $1.19

Granola Bar: $0.89

Total: $4.83--enjoy your snacks!

If you prefer both candy and granola:

Small Popcorn: $2.75

Candy Bar: $1.29

Granola Bar: $0.89

Total: $4.93--enjoy your snacks!

You can check all three-snack combinations involving medium and large popcorns. You will quickly find that none of them will work. All go over budget. You could, however, lead with the cookie:

Cookie: $2.25

Lemonade: $1.19

Candy Bar: $1.29

Total: $4.73--enjoy your snacks!

Cookie: $2.25

Lemonade: $1.19

Granola Bar: $0.89

Total: $4.33--enjoy your snacks!

Cookie: $2.25

Candy Bar: $1.29

Granola Bar: $0.89

Total: $4.43--enjoy your snacks!

Finally, you could get:

Lemonade: $1.19

Candy Bar: $1.29

Granola Bar: $0.89

Total: $3.37--enjoy your snacks!

I hope this helps.