Help please?

Question

For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $12.00 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $14.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Answer 1

Let x = bags of bagels and y = packages of cream cheese
2x + 3y = 12
4x + 2y = 14

Two equestions, two unknowns.
Solve one equation for y:
2y = 14 - 4x
y = 7 - 2x
Now substitute that for y in the first equation:
2x + 3(7 - 2x) = 12
2x + 21 - 6x = 12
-4x = -9
x = 9/4 = $2.25 per bag of bagels

Now plug 2.25 in for x in an equation and solve for y:
4(2.25) + 2y = 14
9 + 2y = 14
2y = 5
y = $2.50 per package of cream cheese.

To check put the values for x and y in each equation:
2(2.25) + 3(2.50) = 12
4.50 + 7.50 = 12
12 = 12 CHECK

4(2.25) + 2(2.50) = 14
9 + 5 = 14
14 = 14 CHECK

Answer 2

let b = bagels
c = cream cheese

2b + 3c = 12
4b + 2c = 14

2b + 3c = 4b + 2c - 2
3c - 2c = 4b - 2b - 2
c = 2b - 2

by substitution:

2b + 3(2b - 2) = 12
2b + 6b - 6 = 12
8b = 18
b = $ 2.25 / bag of bagel

c = 2b - 2
c = 2(2.25) - 2
c = 4.50 - 2
c = $2.50 / bag of cream cheese

Answer 3

2b + 3c = 12 => 4b + 6c = 24
4b + 2c = 14
4c = 10
c = 2.50
b = 2.25