Tina plans on going bowling this weekend, and there are two bowling alleys in her town. the bowling pin charges $5 for shoe rental and $3.50 per game. the alley way charges $3 for shoe rental and $4 per game. write an equation to show the break even point between the two bowling alleys, and then solve the equation. a) 5 + 3.5x = 3 + 4x, x = 4 b) 5 + 3.5x > 3 + 4x, x = 1 c) 5x + 3.5 = 3x + 4, x = 0.25 d) 5x + 3.5 = 3x + 4 x = 2

If I am understanding your question correctly, the cost of shoe rental is fixed and unknown and the price of a game is $4.The question asks to make an equation using the total cost, y, and total games bowled, x. Therefor how we will start out is by plugging the known into the equation y=mx+b. We already m because that is the price per game $4. Therefor y=4x+b. But we still do not know b. The b in y=mx+b is a CONSTANT and usually in linear math equations b is the fixed price. Since we do not know b we have to solve for it. We do know a y, total cost of games, and per an x, number of games. These numbers are $14 and 3 repectively. Therefor we plug them into the equation: y=4x+b14=4(3)+bsolve for b14= 12+b14-12=b2=b
Hope this helps

A) 5 + 3.5x = 3 + 4x, x = 4

Step-by-step explanation:

Let

x = number of gamesy = total price

The relatioship between y and x can be described through a linear equation.

y = m . x + b

where,

m is the slope (here, representing the cost per game)

b is the y-intercept (here, representing the fixed charges)

The equation for the Bowling Pin is:

f(x) = $3.50/game . x + $5 = 3.50 x + 5

The equation fro the Alley Way is:

g(x) = $4/game . x + $3 = 4 x + 3

In the break even point between the two bowling alleys, f(x) = g(x).

3.50 x + 5 = 4 x + 3

5 - 3 = 4 x - 3.50 x

x = 4