Question

6.2 unit 7 test
lupe and her friends spent $20 on snack mix and water. they bought x bags of snack mix for $2.50 each and y bottles of water for $1.25 each. if lupe and her friends bought 11 items, how many bags of snack mix and bottles of water did they buy?
bags of snack mix:
bottles of water:

Explanation:

Step1: Define system of equations

Let $x$ = number of snack mix bags, $y$ = number of water bottles.

$$\begin{cases} x + y = 11 \\ 2.50x + 1.25y = 20 \end{cases}$$

Step2: Isolate $y$ from first equation

Rearrange $x + y = 11$ to solve for $y$.
$y = 11 - x$

Step3: Substitute $y$ into second equation

Replace $y$ in the cost equation.
$2.50x + 1.25(11 - x) = 20$

Step4: Simplify and solve for $x$

Expand and combine like terms.
$2.50x + 13.75 - 1.25x = 20$
$1.25x = 20 - 13.75$
$1.25x = 6.25$
$x = \frac{6.25}{1.25} = 5$

Step5: Calculate $y$ using $x=5$

Use $y = 11 - x$ to find water bottles.
$y = 11 - 5 = 6$

Answer:

bags of snack mix: 5
bottles of water: 6