Question

1. adam bought season passes for six flags. it cost $60 to join, plus $20 for each ticket purchase offer. if he spent a total of $240, how many tickets did adam purchase?

variable ______
equation ______
solution ______

1. josh collects baseball cards. he has four more than twice the number that his brother has. if josh has 48 baseball cards, then how many does his brother have?

variable ______
equation ______
solution ______

1. if the perimeter of the isosceles triangle below is 22, what is the value of x? triangle with two sides 7, base x

equation ______
solution ______

1. if the sum of the angles in a triangle is 180°, what is the value of x? triangle with angles 100°, 30°, 2x

equation ______ image of triangle

1. the windchill in alaska is -13°f and is decreasing 2 degrees each hour. if the temperature is now -21°f, how many hours have passed?

variable ______
equation ______
solution ______

1. taylor joined a meal subscription service. she paid $15 to join, and $10.50 per meal. if she has spent a total of $99, how many meals has she purchased?

variable ______
equation ______
solution ______

Explanation:

Problem 1:

Step1: Define variable

Let \( t \) be the number of tickets Adam purchased.

Step2: Form equation

The total cost is the joining fee plus the cost per ticket times the number of tickets. So the equation is \( 60 + 20t = 240 \).

Step3: Solve for \( t \)

Subtract 60 from both sides: \( 20t = 240 - 60 = 180 \). Then divide both sides by 20: \( t=\frac{180}{20}=9 \).

Step1: Define variable

Let \( b \) be the number of baseball cards his brother has.

Step2: Form equation

Josh has four more than twice the number his brother has, and Josh has 48. So the equation is \( 2b + 4 = 48 \).

Step3: Solve for \( b \)

Subtract 4 from both sides: \( 2b = 48 - 4 = 44 \). Then divide both sides by 2: \( b=\frac{44}{2}=22 \).

Step1: Define variable

The triangle has two sides of length \( y \) and one side of length \( x \), perimeter \( P = 2y + x \). Wait, from the diagram, it's an isosceles triangle with two sides \( y \) and base \( x \), perimeter is \( y + y + x=2y + x \). Given perimeter is 22, so equation is \( 2y + x = 22 \)? Wait, maybe the diagram has two sides as \( y \) and one as \( x \), but maybe the triangle is isosceles with two sides \( y \) and base \( x \), but if we assume maybe the triangle has sides \( y, y, x \), perimeter \( 2y + x = 22 \). But maybe the diagram is a triangle with two sides \( y \) and one \( x \), but without knowing \( y \), wait maybe it's a typo or maybe the triangle has sides \( y, y, x \), but perhaps the original problem has \( y \) as a known? Wait, maybe the triangle is isosceles with two sides 7 (assuming the diagram has 7,7,x). Let's assume the two equal sides are 7, so perimeter \( 7 + 7 + x = 22 \).

Step1: Define variable

Let \( x \) be the base length.

Step2: Form equation

Perimeter of triangle: \( 7 + 7 + x = 22 \) (assuming equal sides are 7).

Step3: Solve for \( x \)

Simplify: \( 14 + x = 22 \). Subtract 14: \( x = 22 - 14 = 8 \).

Answer:

Variable: \( t \) (number of tickets)
Equation: \( 60 + 20t = 240 \)
Solution: \( t = 9 \)

Problem 2: