The problem statement gives two relations between the prices of two kinds of tickets. These can be used to write a system of equations for the ticket prices.

<h3>setup</h3>

Let 'a' and 'c' represent the prices of adult and children's tickets, respectively. The given relations can be expressed as ...

a - c = 1.50 . . . . . . . adult tickets are $1.50 more

175a +325c = 3512.5 . . . . . total revenue from ticket sales.

<h3>solution</h3>

We are only interested in the price of an adult ticket, so we can eliminate c to give one equation we can solve for 'a'. Using the first equation, an expression for c is ...

c = a -1.50

Substituting that into the second equation, we have ...

175a +325(a -1.50) = 3512.50

500a -487.50 = 3512.50 . . . . . . simplify

500a = 4000 . . . . . . add 487.50

a = 8 . . . . . . . . . divide by 500

An adult ticket costs $8.

5 0

2 years ago

7. The length of a minute hand of a clock is 3.5cm. Find the angle it turns through if it

babymother [125]

Answer:

The angle it turns through if it sweeps an area of 48 cm² is 448.8°

Step-by-step explanation:

If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it sweeps an area of 48 cm, we will follow the steps below;

area of a sector = Ф/360 × πr²

where Ф is the angle, r is the radius π is a constant

from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5

Ф =? area of the sector= 48 cm² π = $\frac{22}{7}$

we can now go ahead to substitute the values into the formula and solve Ф

area of a sector = Ф/360 × πr²

48 = Ф/360 × $\frac{22}{7}$ × (3.5)²

48 = Ф/360 × $\frac{22}{7}$ ×12.25

48 = 269.5Ф / 2520

multiply both-side of the equation by 2520

48×2520 = 269.5Ф

120960 = 269.5Ф

divide both-side of the equation by 269.5

448.8≈Ф

Ф = 448.8°

The angle it turns through if it sweeps an area of 48 cm² is 448.8°

7 0

3 years ago