It costs 3 tickets to play a game at the fair. if you spent 21 tickets on the game, which equation could you use to solve for the number of games, g? a. 21g=3 b. 21·3=g c. g3=21 d. 3g=21

Option D. 3g=21

Step-by-step explanation:

Let

g -----> the number of games

we know that

The number of games multiplied by 3 tickets to play a game must be equal to 21 tickets

so

The linear equation that represent this problem is

solve for g

Divide by 3 both sides

The value of b is 9.5

Step-by-step explanation:

If a system of equations has infinitely  many solutions, that means the two equations are equal

If the system of equations ax + by = c, dx + ey = f, then

Let us use this fact to solve the question

∵ 3x - y = 19 ⇒ (1)

∵ 1.5x - 0.5 y = b ⇒ (2)

∵ This system of equations has infinitely many solutions

∴ The coefficients of x must be equal

∴ The coefficients of y must be equal

∴ The numerical terms must be equal

→ Multiply equation (2) by 2 to make the coefficients of x and y on it

  equal the coefficients of x and y in equation (1)

∵ 2(1.5x) - 2(0.5y) = 2(b)

∴ 3x - y = 2b ⇒ (3)

→ By comparing equations (1) and (3), 19 must equal 2b

∵ 2b = 19

→ Divide both sides by 2

∴ b = 9.5

∴ The value of b is 9.5