6 James bought 16 tickets for a concert. The good tickets cost $8 and bad tickets
cost $5. He spent a total of $113 on all the tickets. Write a system that can be used to
determine how many good tickets James bought and how many bad ticket he bought.

James bought 11 good tickets and 5 bad tickets.

Step-by-step explanation:

Given that:

Cost of each good ticket = $8

Cost of each bad ticket = $5

Total amount spent = $113

Total tickets bought = 16

Let,

x be the number of good tickets bought

y be the number of bad tickets bought

x+y=16     Eqn 1

8x+5y=113    Eqn 2

Multiplying Eqn 1 by 5

5(x+y=16)

5x+5y=80    Eqn 3

Subtracting Eqn 3 from Eqn 2

(8x+5y)-(5x+5y)=113-80

8x+5y-5x-5y=33

3x=33

Dividing both sides by 3

Putting x=11 in Eqn 1

11+y=16

y=16-11

y=5

Hence,

James bought 11 good tickets and 5 bad tickets.

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.

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