A promoter needs to make $89,900 from the sale of 3200 tickets. She charges $25 for some tickets and $58 for the others. (a) If there are x of the $25 tickets sold and y of the $58 tickets sold, write an equation that states that the sum of the tickets sold is 3200. (b) How much money is received for the sale of x tickets for $25 each? (c) How much money is received for the sale of y tickets for $58 each? (d) Write an equation that states that the total amount received from the sale is $89,900. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $89,900.

a) x + y = 3200... Equation 1

b) $72,500

c) $17,400

d) 25x + 58y = 89,900 Equation 2

Step-by-step explanation:

A promoter needs to make $89,900 from the sale of 3200 tickets. She charges $25 for some tickets and $58 for the others.

Hence, the system of Equations is given as:

Let the

Number of the $25 tickets sold = x

Number of the $58 tickets sold = y

Hence:

x + y = 3200... Equation 1

x = 3200 - y

$25 × x + $58 × y= $89,900

25x + 58y = 89,900 Equation 2

Substitute 3200 - y for x

25(3200 - y ) + 58y = 89,900

80,000 - 25y + 58y = 89,900

- 25y + 58y = 89,900 - 80,000

33y = 9,900

y = 9,900/33

y = 300 tickets

Solving for x

x = 3200 - y

x = 3200 - 300

x = 2900 tickets

(a) If there are x of the $25 tickets sold and y of the $58 tickets sold, write an equation that states that the sum of the tickets sold is 3200.

x + y = 3200... Equation 1

(b) How much money is received for the sale of x tickets for $25 each?

x = 2900 tickets

Hence:

$25 × 2900 tickets

= $72,500

(c) How much money is received for the sale of y tickets for $58 each?

y = 300 tickets

Hence:

$58 × 300

= $17,400

(d) Write an equation that states that the total amount received from the sale is $89,900.

25x + 58y = 89,900 Equation 2

(e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $89,900.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.