Question

Pete purchased 5 drinks and 6 snacks and spent a total of $22.50. Jaime purchased 1 drink and 9 snacks and spent a total of 24.75 each drink costs the same amount. Each snack costs the same amount write a system of linear equations that can be used to find thr coet of one drink and one snack.

Answer 1

`5x+6y=22.50\\x+9y=24.75`

Explanation:

Cost of 5 drinks and 6 snacks = $22.50

Cost of 1 drink and 9 snacks = $24.75

Each drink costs the same and each snack costs the same.

Let cost of each drink = $
`x`

Let cost of each snack = $
`y`

As per the question, writing the system of equations:

`5x+6y=22.50 ...... (1)\\x+9y=24.75 ...... (2)`

Let us use elimination method, to find the cost of each drink and cost of each snack.

Multiplying equation (2) by 5 and then subtracting equation (1) from it:

`45y - 6y = 123.75 - 22.5 \\\Rightarrow 39y = 101.25\\\Rightarrow y \approx \$2.60`

Using equation (1):

`5x+2.6 * 6 = 22.5\\\Rightarrow 5x = 22.5 - 15.6\\\Rightarrow 5x = 6.9\\\Rightarrow x = \$1.38`

Cost of each drink = $1.38

Cost of each snack = $2.60