Question

Like many teenagers struggling with peer pressure and the desire to be cool, Janis started secretly smoking cigarettes. Janis’s parents give her an allowance of $385 per month to buy a sandwich for lunch at school every day. Janis likes to consume her sandwiches in fixed proportions with cigarettes. She eats exactly 3 sandwiches for every pack of cigarettes that she smokes. The price of cigarettes is $3 per pack and the price of sandwiches is 4 per sandwich.

If Janis's parents reduce her income from $385 to $180, by how many packs will her consumption of cigarettes be reduced? Round your final answer to one decimal place.

Answer 1

Initial income =$385

Pc=3 and Ps=4

Pc is price of a pack of cigarettes and Ps is the price of sandwiches

Budget line:

3C+4S =385

Proportion:

C/S = 1/3

Here C is the quantity of pack of cigarettes and S is the quantity of sandwiches.

By solving it:

3C=S

Use the above relation into budget line:

3C+4(3C) =385

15C =385

C=385/15

C= 77/3

If Janis's parents reduce her income from $385 to $180 then

New budget line:

3C+4S=180

Relation: 3C=S

Use above relation in new budget line:

3C+12C=180

C=180/15

C= 36/3

Her consumption of cigarette decrease by= 77/3 - 36/3= 41/3 packs