A word problem.?

Question

Ok I reallly need help with a problem so here it is.

Alli is buying some sport drinks for her team. At the vending machines, there are 12 oz. bottles for .60. At the corner store, there are 20 oz. bottles for .95 cents.At the grocery store, there are 32 oz. bottles for $1.45.

Where can Alli get the most juice?
Is it the best buy?
If Alli visted more than one place, where can she get the most juice for her money?

Please try to show your work. Thanks!

YOU HAVE 4.25 to spend

Answer 1

let:
x be the # of bottle to be bought in vending machine
y be the # of bottle to be bought in corner store
z be the # of bottle to be bought in grocery store

Since Alli only have $4.25 to spend and # of bottle should be integer, so the contraints are:
0.6x + 0.95y + 1.45z < 4.25
x is an integer between 0 to 7 (Alli doesn't have enough money to buy 8 bottles from the vending machine)
y is an integer between 0 to 4
z is an integer between 0 to 2

Since the inequality involves 3 variables, so it will be easier to set up 3 scenerio, when z= 0, 1 or 2.

So, for the first scenerio z=0 (given that no bottle is bought from grocery store)
then the formula will become 0.6x + 0.95Y < 4.25

Then, for the second scenerio z=1 (given that 1 bottle is bought from grocery store), Alli only have $2.8 left to spend since Alli spend $1.45 at the grocery store already
then the formula will become 0.6x + 0.95Y < 2.80

Finally, for the third scenerio z=2 (given that 2 bottles is bought from grocery store), Alli only have $1.35 left to spend since Alli spend $2.90 at the grocery store already
then the formula will become 0.6x + 0.95Y < 1.35

By finding the possible values of x, y and z. You can then figure out which combination will provide the maximum volume of juice can be purchased.

Answer 2

Compute the price per oz

vending =.6/12 = .05
corner = .95/20 = 0.0475
grocery =1.45/32 = .0453

The best buy is the grocery store.

Most juice:
Since she has 4.25 to spend, she must buy in the increments each source offers.


vending = Integer(4.25/.6)*12 = 84oz
corner= Integer(4.25/.95)*20 = 80 oz
grocery= Integer(4.25/1.45)*32=64 oz


Most for her money
The third question is to figure out how to buy the most juice for the money by spending close to 4.25

Max(x*12 + y *20 + z*32)
Where x*.6 + y *.95 + z*1.45 <= 4.25

x=2 y = 0 z=2
88 oz $4.10

j

Answer 3

The 32 oz bottles are 4.53 cents/oz - $1.45/32=.0453125
The 20 oz bottles are 4.75 cents/oz - .95/20=.0475
The 12 oz bottle are 5 cents/oz .60/12=.05

So the best deal is the 32 oz bottles

She can get 84 oz (7x12oz)at the vending machine for $4.20 (7x.60)
She can get 80 oz (4x20)at the corner store for $3.80 (4x.95)
She can get 64 oz (2x32) at the grocery for $2.90 (2x 1.45)

The best combo is 84oz for $3.95
1 32 oz $1.45
2 20 oz $1.90
1 12 oz $.60

Answer 4

First figure out how much she is paying per ounce at each place:
Vending machine: .6/12 = .05 cents per ounce
Corner store: .95/20 = .048 (about .05 cents per ounce)
Grocery Store: 1.45/32 = .092 (about .09 cents per ounce)

She can get the most juice at the Grocery Store, but it is not the best buy because she is paying more per ounce.

She can get the most juice for her money at the corner store or the Vending machine

Answer 5

divide the pence by the number of ounces to find out how much per ounce each is to find out the best value
you dont actually say how much she needs or how much she has to spend so the only question that can be answered by this is which is the best value sorry!

Answer 6

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