**Applying addition and subtraction of integers :**

We can use what you know about adding and subtracting integers to solve real world problems.

**Example 1 : **

A seal is swimming in the ocean 5 feet below sea level. It dives down 12 feet to catch some fish. Then, the seal swims 8 feet up towards the surface with its catch. What is the seal’s final elevation relative to sea level ?

**Solution : **

**Step 1 : **

The seal starts at 5 feet below the surface, so its initial position is -5 ft.

Write an expression.

Starts - Dives down + Swims up

-5 - 12 + 8

**Step 2 : **

Add or subtract from left to right to find the value of the expression.

-5 - 12 + 8 = -17 + 8

= -9

The seal’s final elevation is 9 feet below sea level.

**Example 2 : **

Anna is in a cave 40 feet below the cave entrance. She descends 13 feet, then ascends 18 feet. Find her new position relative to the cave entrance.

**Solution : **

**Step 1 : **

Anna starts at 40 feet below cave entrance, so her initial position is -40 ft.

Write an expression.

Starts - Descends + Ascends

-40 - 13 + 18

**Step 2 : **

Add or subtract from left to right to find the value of the expression.

-40 - 13 + 18 = -53 + 18

= -35

Anna's new position is 35 feet below the cave entrance.

**Example 3 : **

Tomas works as an underwater photographer. He starts at a position that is 15 feet below sea level. He rises 9 feet, then descends 12 feet to take a photo of a coral reef. Write and evaluate an expression to find his position relative to sea level when he took the photo.

**Solution : **

**Step 1 : **

Tomas starts at 15 feet below sea level, so his initial position is -15 ft.

Write an expression.

Starts + Rises - Descends

-15 + 9 - 12

**Step 2 : **

Add or subtract from left to right to find the value of the expression.

-15 + 9 - 12 = -6 - 12

= -18

When Tomas takes photo, his position is 18 feet below the sea level.

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