Question

1. andre wrote the expression -2 + 4x ÷ 3 to represent the relationship shown in the table. write two other expressions that also represent the relationship shown in the table. 17. higher order thinking to rent a car for a trip, four friends are combining their money. the group chat shows the amount of money that each puts in. one expression for their total amount of money is 189 plus p plus 224 plus q. a. use the commutative property to write two equivalent expressions. b. if they need $500 to rent a car, find at least two different pairs of numbers that p and q could be. 18. which expressions are equivalent to \\(\frac{3}{5}x + 3\\)? select all that apply. \\(\frac{2}{5}x + 3\frac{1}{5}x\\)

Explanation:

17a.

Step1: Recall Commutative Property

The Commutative Property of Addition states that for any numbers \(a\), \(b\), \(a + b = b + a\). The original expression is \(189 + p + 224 + q\).

Step2: Rearrange terms (First equivalent)

Using the Commutative Property, we can swap \(189\) and \(p\) to get \(p + 189 + 224 + q\).

Step3: Rearrange terms (Second equivalent)

We can also swap \(224\) and \(q\) in the original expression to get \(189 + p + q + 224\).

Step1: Find the total of known amounts

First, calculate the sum of \(189\) and \(224\). \(189+224 = 413\).

Step2: Set up the equation

The total amount of money is \(189 + p + 224 + q=413 + p + q\), and this should equal \(500\). So, \(413 + p + q = 500\), which simplifies to \(p + q=500 - 413=87\).

Step3: Find pairs of \(p\) and \(q\)

We need to find pairs of numbers \(p\) and \(q\) such that their sum is \(87\).

• First pair: Let \(p = 10\), then \(q = 87 - 10 = 77\) (since \(10+77 = 87\)).
• Second pair: Let \(p = 20\), then \(q = 87 - 20 = 67\) (since \(20 + 67=87\)).

Answer:

Two equivalent expressions are \(p + 189 + 224 + q\) and \(189 + p + q + 224\) (other valid rearrangements are also acceptable).

17b.