Question

the tennis club is selling water bottles and hats to raise money for a tennis tournament. a water bottle costs $4 and a hat costs $6 the club wants to raise $1,200

Answer 1

Let's call the amount of water bottles sold as x and the amount of hats sold as y.

Item 15:

The amount of money raised selling water bottles is given by the product between the unitary cost($4) of a water bottle by the amount of water bottles sold(x). The same logic can be applied to the money raised selling hats. The total amount of money raised is given by the sum of those products.

Since the club wants to raise $1,200, the following equation describes our problem

`4x+6y=1200`

item 16:

Since we chose the amount of water bottles sold as x and the amount of hats sold as y, the horizontal axis label will be "water bottles" and the vertical axis label will be "hats".

To find three points that belongs to this line, we just need to evaluate some values on the equation we found on item 15.

The easiest points to calculate are the intercepts(when x = 0 and when y = 0).

The y-coordinate of the y-intercept is

`\begin{gathered} 4\cdot0+6y=1200 \\ 6y=1200 \\ y=(1200)/(6) \\ y=200 \end{gathered}`

The point (0, 200) belongs to this line.

The x-coordinate of the x-intercept is

`\begin{gathered} 4x+6\cdot0=1200 \\ x=(1200)/(4) \\ x=300 \end{gathered}`

The point (300, 0) belongs to this line.

Solving the item 17, we want to calculate the amount of hats if 150 water bottles are sold. To find this point we just need to evaluate x = 150 on our equation.

`\begin{gathered} 4(150)+6y=1200 \\ 600+6y=1200 \\ 6y=1200-600 \\ 6y=600 \\ y=(600)/(6) \\ y=100 \end{gathered}`

The point (150, 100) belongs to this line.

Using those 3 distinct points, the graph of this equation is

item 17:

From the previous item, we already have the answer.

The tennis club must sell 100 hats.