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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.

BWhen 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.

Verified Answer :

texaschic101
  1. 3t + 2b = 16....multiply 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 = 75......d = 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 = 23....so there are 23 quarters
    =====================
    x = 2 point shots, y = 3 point shots
    x + y = 24.....multiply by -2
    2x + 3y = 54
    ----------------
    -2x - 2y = -48 (result of multiplying by -2)
    2x + 3y = 54
    ----------------add
    y = 6.......so there was 6 three point shots

    x + y = 24
    x + 6 = 24
    x = 18......and 18 two point shots
    ======================
    5.50g + 5 = 2.50g + 17
    5.50g - 2.50g = 17 - 5
    3g = 12
    g = 4......they will cost the same with 4 game rentals
    less then 4 rentals, use Fun Guys....more 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

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