Question

1. write two expressions that represent the area of the rectangular region.

(there is a rectangle divided into two small rectangles, the height of the big rectangle is 3, the width of the left small rectangle is 2x, the width of the right small rectangle is 5)

1. ava runs m miles each day for 4 days. each day, lily runs 2 more miles than ava.

a. write an expression that represents the number of miles lily runs in those 4 days.
b. evaluate the expression from part (a) when m = 1. interpret the result.
c. write an expression equivalent to the one from part (a) by using a tabular model.
d. determine the number of miles lily runs in 4 days when ava runs 3 miles each day.

1. logan mows l lawns each week for 8 weeks. eve mows 2 fewer lawns than logan each week.

a. write an expression that represents the number of lawns eve mows in those 8 weeks.

Explanation:

Problem 1

Step 1: Area of two rectangles

The first rectangle has length \(2x\) and width \(3\), so its area is \(3\times2x = 6x\). The second rectangle has length \(5\) and width \(3\), so its area is \(3\times5=15\). The total area is the sum of these two areas: \(6x + 15\).

Step 2: Area of the big rectangle

The total length of the big rectangle is \(2x + 5\) and the width is \(3\). So the area is \(3\times(2x + 5)\).

Step 1: Miles Lily runs per day

Ava runs \(m\) miles each day, and Lily runs \(2\) more miles than Ava each day. So Lily runs \(m + 2\) miles per day.

Step 2: Miles Lily runs in 4 days

To find the total miles Lily runs in 4 days, we multiply the miles per day by 4. So the expression is \(4(m + 2)\).

Step 1: Substitute \(m = 1\) into the expression

We have the expression from part (a) as \(4(m + 2)\). Substitute \(m = 1\) into it: \(4(1 + 2)\).

Step 2: Calculate the value

First, calculate inside the parentheses: \(1+2 = 3\). Then multiply by 4: \(4\times3=12\). Interpretation: When Ava runs 1 mile each day, Lily runs a total of 12 miles in 4 days.

Answer:

First expression: \(6x + 15\); Second expression: \(3(2x + 5)\)

Problem 2a