Question

Diego's neighbors paid him to take care of their fish when they went on vacation. He spent $13 of his earnings on a book and $9 on some art supplies. Afterward, he had at most $10 left.

Part A.) Write an inequality to represent how much Diego's neighbors paid him.

Part B.) Solve the inequality.

(this is solving inequalities using addition or subtraction)

Answer 1

The inequality representing the amount Diego was paid is x - 13 - 9 ≤ 10. By simplifying this inequality, we find out Diego's neighbors paid him at most $32 for taking care of their fish.

Step-by-step explanation:

To answer the student's question, let's establish the variables and the inequality:

Let x represent the total amount Diego's neighbors paid him for taking care of their fish. Diego spent $13 on a book and $9 on some art supplies. After these purchases, he had at most $10 left. This situation can be represented by the following inequality:

Part A.)

The inequality is x - 13 - 9 ≤ 10.

Part B.)

To solve the inequality, we'll combine the constants and simplify:

1. x - 22 ≤ 10 (Combine like terms)
2. x ≤ 10 + 22 (Add 22 to both sides)
3. x ≤ 32 (Simplify)

This means that Diego was paid at most $32 by his neighbors for taking care of their fish.

Answer 2

A: 9 + 13 + 10 is equal to or less than C

B: 32 is equal to or less than C

Step-by-step explanation:

How I got A:

in order to solve this you have to add 9, 13, and 10.

don't solve it right away, but write every number out individually.

It says in the problem, "Afterward he had AT MOST $10".

With this we know we need a sign other than equal to.

if the amount was at most $10, we need to use equal to or less than.

I chose equal to or less than because it says AT MOST, so the amount he was pain will be equal to, or less than all of then numbers given to us added.

How I got B:

I added 9, 13, and 10.

The sum of these numbers is 32

C is our variable, because we don't know how much they paid him

32 is equal to or less than C

Hope this helps <3