# Adding Integers in Applications

## Adding Integers in Applications

Recall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of $$\text{\5}$$ could be represented as $$\text{−\5.}$$ Let’s practice translating and solving a few applications.

Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.

## Example

The temperature in Buffalo, NY, one morning started at $$7\phantom{\rule{0.2em}{0ex}}\text{degrees}$$ below zero Fahrenheit. By noon, it had warmed up $$12\phantom{\rule{0.2em}{0ex}}\text{degrees}.$$ What was the temperature at noon?

### Solution

We are asked to find the temperature at noon.

 Write a phrase for the temperature. The temperature warmed up 12 degrees from 7 degrees below zero. Translate to math notation. −7 + 12 Simplify. 5 Write a sentence to answer the question. The temperature at noon was 5 degrees Fahrenheit.

## Example

A football team took possession of the football on their $$\text{42-yard line.}$$ In the next three plays, they lost $$\text{6 yards,}$$ gained $$\text{4 yards,}$$ and then lost $$\text{8 yards.}$$ On what yard line was the ball at the end of those three plays?

### Solution

We are asked to find the yard line the ball was on at the end of three plays.

 Write a word phrase for the position of the ball. Start at 42, then lose 6, gain 4, lose 8. Translate to math notation. 42 − 6 + 4 − 8 Simplify. 32 Write a sentence to answer the question. At the end of the three plays, the ball is on the 32-yard line.