Question

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.

Answer 1

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
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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
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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
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(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)
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sorry..not 100% sure about the bonus