40 points
sylvester and lin go to the amusement park. sylvester plays 5 rounds of mini golf and takes 4 turns in the batting cages for $60. lin plays 3 rounds of mini golf and takes 6 turns in the batting cages for $45. use two equations to find the price for each activity. enter your answers in the boxes.

minigolf = 10

batting cage 2.50

Step-by-step explanation:

Let g= rounds of golf

Let b = batting cage

Sylvester

5g+4b = 60

Lin

3g +6b = 45

We have two equations and two unknowns

5g+4b = 60

3g +6b = 45

Divide the second equation by 3

3/3g +6/3b = 45/3

g+2b = 15

Multiply this equation by -2

-2g -4b = -30

Add this to the first equation

5g+4b = 60

-2g -4b = -30

3g = 30

Divide by 3

3g/3 = 30/3

g = 10

A game of mingolf is 10 dollars

Now we need to find b

g+2b = 15

10 +2b =15

Subtract 10

10-10+2b =15-10

2b =5

Divide by 2

2b/2 =5/2

b = 2.5

A turn in the batting cage is 2.50

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]