At the local market, bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while sarah buys 2 juice boxes and 1 hot dog at a cost of $5.
the cost of each juice box is $? , and the cost of each hot dog is $? .

The cost of each juice boxes is $ 2

The cost of each hot dogs is $ 1  .

Step-by-step explanation:

Given as :

The amount which Bill pays for 3 juice boxes and 2 hot dogs = $ 8

The amount which Sarah pays for 2 juice boxes and 1 hot dogs = $ 5

Let The cost of each juice boxes = $ j

And The cost of each hot dogs = $ h

Now, According to question

3 j + 2 h = 8               .........A

2 j + 1 h = 5                 ..........B

Now, solving the equations

2 × (  2 j + 1 h ) = 2 × 5

or, 4 j + 2 h = 10

I.e ( 4 j + 2 h ) - ( 3 j + 2 h ) = 10 - 8

Or, ( 4 j - 3 j ) + ( 2 j - 2 h ) = 2

Or, j + 0 = 2

∴  j = 2

So , The cost of each juice boxes = j = $ 2

Now, Put the value of j in Eq A

I.e  3 × 2 + 2 h = 8

Or, 6 + 2 h = 8

Or. 2 h = 8 - 6

or, 2 h = 2

∴   h = = 1

So, The cost of each hot dogs = h = $ 1

Hence The cost of each juice boxes is $ 2

And The cost of each hot dogs is $ 1  . Answer

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80