Question

Two hiking groups made the purchases shown below. What is the cost of each item. GROUP 1: 6 muffins, 12 granola bars, Total=$26.70 GROUP 2: 8 muffins, 15 granola bars, Total=34.00

Answer 1

Price of each muffin = $1.25

Price of each granola bar = $1.6

Explanation:

Group 1:

6 muffins, 12 granola bars

Total money paid = $26.70

Group 2:

8 muffins, 15 granola bars,

Total money paid = $34.00

To find:

Price of each item?

Solution:

Let the price of one muffin = $
`x`

Let the price of one granola bar = $
`y`

As per group 1, the equation can be written as:

`6x+12y=26.70\\\Rightarrow x+2y=4.45 .... (1)`

As per group 2, the equation can be written as:

`8x+15y = 34` .... (2)

Let us use elimination method to solve for
`x` and
`y`.

Multiplying equation (1) with 8 and subtracting (2) from it:

`16y-15y = 35.6 - 34\\\Rightarrow y = 1.6`

Using equation (1):

`x+3.2=4.45\\\Rightarrow x = 1.25`

Therefore, the answer is:

Price of each muffin = $1.6

Price of each granola bar = $1.25