Solve by substitution, elimination, or graphing. show your work.
1.) mike and jc went to taco tent. mike bought 3 tacos and 2 burritos for $16. jc bought 5 tacos and 3 burritos for $25.
2.) there are 75 coins consisting of dimes and quarters with a value of $10.95. how many dimes are there? how many quarters are there?
3.)kade made 24 shots in the basketball game. all, either 2 or 3 point shots. if he scored 54 points, how many of each did he make? write 2 equations, solve by elimination.
4.) the fun guys game rental store charges an annual fee of $5 plus $5.50 per game rented. the game bank charges an annual fee of $17 plus $2.50 per game.
a)for how many game rentals will the cost be the same at both stores? *write the cost equations for each and solve by graphing, substitution, or elimination.
b) when would you use each company?
5.) a)find the equation of line a in y=mx+b with points (2,5) (4,9)
b)find the equations of line b in y=mx+b with points (0,5) (3,8)
c)find the point at which the two lines intersect.
bonus) each side of a square is 2x+y and each side of an equilateral triangle is 2x+3y. their perimeters are both 48inches. find x and y.

1. 3t + 2b = 16multiply by -3
    5t + 3b = 25...multiply by 2
   
    -9t - 6b = -48 (result of multiplying by -3)
    10t + 6b = 50 (result of multiplying by 2)
  add
   t = 2

3t + 2b = 16
3(2) + 2b = 16
2b = 10
b = 5

so tacos (t) cost $ 2 and burritos (b) cost $ 5

d + q = 75d = 75 - q
0.10d + 0.25q = 10.95

0.10(75 - q) + 0.25q = 10.95
7.50 - 0.10q + 0.25q = 10.95
0.15q = 3.45
q = 23so there are 23 quarters

x = 2 point shots, y = 3 point shots
x + y = 24multiply by -2
2x + 3y = 54

-2x - 2y = -48 (result of multiplying by -2)
2x + 3y = 54
add
y = 6so there was 6 three point shots

x + y = 24
x + 6 = 24
x = 18and 18 two point shots

5.50g + 5 = 2.50g + 17
5.50g - 2.50g = 17 - 5
3g = 12
g = 4they will cost the same with 4 game rentals
less then 4 rentals, use Fun Guysmore then 4, use Game Bank

(2,5)(4,9)
slope = (9 - 5) / (4 - 2) = 4/2 = 2

y = mx + b
slope(m) = 2
(2,5)...x = 2 and y = 5
now sub and find b, the y int
5 = 2(2) + b
5 = 4 + b
5 - 4 = b
1 = b
so ur equation is : y = 2x + 1 (line A)

(0,5)(3,8)
slope = (8 - 5) / (3 - 0) = 3/3 = 1

y = mx + b
slope(m) = 1
(0,5)...x = 0 and y = 5
now sub
5 = 1(0) + b
5 = b
so ur equation is : y = x + 5 (line B)

y = 2x + 1
y = x + 5

2x + 1 = x + 5
2x - x = 5 - 1
x = 4

y = 2x + 1
y = 2(4) + 1
y = 8 + 1
y = 9
so they will meet at (4,9)

sorry..not 100% sure about the bonus

    

ABD = 180 - 65 = 115 degrees

ADB = 180 - 45 - 115 = 20 degrees

First box, no check.

ACD is 90 degrees, so

second box, no check

Law of Sines:

AB / sin ADB = AD / sin ABD

AD = AB (sin ABD / sin ADB ) = 18 (sin 115 / sin 20) = 47.6976

ACD is an isosceles right triangle so

CD = 47.6976/√2 = 33.7

CD=33.7, CHECK

sin 65 = CD/BD

BD = CD/sin 65 = 33.7/sin 65 = 37.2

BD=37.2 CHECK