A school reserved a banquet hall for the spring dance. In addition to a $100 deposit, each couple must pay $20. If the total cost of the banquet hall is $1, 140. Compare and contrast the steps you used to solve the problem algebraically and arithmetically.

Step-by-step explanation:

1.)20x + 100 = 1440

-Let the number of couples be x. So, the total amount paid by all the couple’s are $20x. School paid $100 as security, so the total amount paid is

$ (20x + 100)

2.) 20x = 1440 - 100 ⇒ 20x = 1040

X = 52

3. ) The security money  is $100, so the couples paid $1440- 100 = $1040 in total. As the couples paid $ 20 each than- = 52

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.