Answer to Question #94405 in Algebra for Mychal

Question

I am at the store debating between cinnamon rolls I want to buy. There are two options: A 4 pack of individual rolls or a sheet of 6 rolls. The 4 pack is 1 dollar more than the sheet of 6. I decide to buy two sheets of 6 rolls and three 4 packs of individual rolls. My total bill is $16.75. How many do the 4 pack and sheet of 6 rolls cost?

Answer 1

Let x be the cost of one 4-rolls pack and y be the cost of one 6-rolls pack.

Then x=y+1 (1) (since the smaller pack costs 1$ more than the bigger pack).

Also, 3x+2y =16.75 (2)

We can solve this system with two equations using substitution method.

Namely, we plug the expression of x from (1) in (2):

3(y+1)+2y=16.75

3y + 3 +2y =16.75

5y +3 =16.75

Then 5y = 16.75 -3 =13.75

Then y = 13.75/ 5 = 2.75 & x=y+1=3.75

In conclusion, one 4-rolls pack costs $3.75 and one 6-rolls pack costs $2.75