Question

1. a group of 4 friends went to the movies. in addition to their tickets, they bought a large bag of popcorn to share for $6.25. the total was $44.25. a. write and solve an equation to find the cost of one movie ticket, m. b. draw a model to represent the equation.

Explanation:

Step1: Set up the equation

The cost of 4 movie - tickets ($4m$) plus the cost of popcorn ($6.25$) equals the total cost ($44.25$). So the equation is $4m + 6.25=44.25$.

Step2: Isolate the term with the variable

Subtract 6.25 from both sides of the equation: $4m+6.25 - 6.25=44.25 - 6.25$. This simplifies to $4m = 38$.

Step3: Solve for m

Divide both sides of the equation by 4: $\frac{4m}{4}=\frac{38}{4}$. So $m = 9.5$.

Answer:

a. The equation is $4m + 6.25 = 44.25$ and the cost of one movie - ticket $m = 9.5$.
b. For the model, we can draw 4 rectangles to represent the 4 movie - tickets (label each rectangle as $m$), and a circle to represent the popcorn with a value of $6.25$. Then draw a large rectangle around them to represent the total cost of $44.25$.