Kara has 21 collectible buttons to sell. she sells the small buttons for $3 and the large buttons for $4, and earns a total of $68. if the small buttons are represented by x and the large buttons are represented by y, which of the following systems of equations can be used to calculate the number of large and small buttons sold?
a.) x + y = 21, 3x + 4y = 68
b.) x + y = 68, 3x + 4y = 21
c.) x + y = 21, 4x + 3y = 68
d.) x + y = 68, 4x + 3y = 21

i can you, i love poetry

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.