The Subtraction and Addition Properties of Equality

Example 2.11

How to Solve Translate and Solve Applications

The MacIntyre family recycled newspapers for two months. The two months of newspapers weighed a total of 57 pounds. The second month, the newspapers weighed 28 pounds. How much did the newspapers weigh the first month?

Solution

Step 1. Read the problem. Make sure all the words and ideas are understood.	The problem is about the weight of newspapers
Step 2. Identify what we are asked to find.	What are we asked to find?	How much did the newspapers weigh the 2nd month?
Step 3. Name what we are looking for. Choose a variable to represent that quantity	Choose a variable.	Let w equal weight of the newspapers the 1st month.
Step 4. Translate into an equation. It may be helpful to restate the problem in one sentence with the important information.	Restate the problem. We know that the weight of the newspapers the second month is 28 pounds.	Weight of newspapers the 1st month plus the weight of the newspapers the 2nd month equals 57 pounds. Weight from 1st month plus 28 equals 57. \(w + 28 = 57\)
Step 5. Solve the equation using good algebra techniques.	Solve.	\(w+28-28=57-28\) \(w=29\)
Step 6. Check the answer and make sure it makes sense.	Does 1st month's weight plus 2nd month's weight equal 57 pounds?	Check: Does 1st month's weight plus 2nd month's weight equal 57 pounds? \(29 + 28 \stackrel{?}{=} 57\) \(57 = 57\)
Step 7. Answer the question with a complete sentence.	Write a sentence to answer "How much did the newspapers weigh the 2nd month?"	The 2nd month the newspapers weighed 29 pounds.

Try It 2.21

Translate into an algebraic equation and solve:

The Pappas family has two cats, Zeus and Athena. Together, they weigh 23 pounds. Zeus weighs 16 pounds. How much does Athena weigh?

Try It 2.22

Translate into an algebraic equation and solve:

Sam and Henry are roommates. Together, they have 68 books. Sam has 26 books. How many books does Henry have?

How To

Solve an application.

Step 1. Read the problem. Make sure all the words and ideas are understood.

Step 2. Identify what we are looking for.

Step 3. Name what we are looking for. Choose a variable to represent that quantity.

Step 4. Translate into an equation. It may be helpful to restate the problem in one sentence with the important information.

Step 5. Solve the equation using good algebra techniques.

Step 6. Check the answer in the problem and make sure it makes sense.

Step 7. Answer the question with a complete sentence.

Example 2.12

Randell paid $28,675 for his new car. This was $875 less than the sticker price. What was the sticker price of the car?

Solution

Step 1. Read the problem.
Step 2. Identify what we are looking for.	"What was the sticker price of the car?"
Step 3. Name what we are looking for. Choose a variable to represent that quantity.	Let s= the sticker price of the car.
Step 4. Translate into an equation. Restate the problem in one sentence.	$28,675 is $875 less than the sticker price
Step 5. Solve the equation.	$28,675 is $875 less than \(s \) \(28,675=s−875\) \(28,675+875=s−875+875\) \(29,550=s\)
Step 6. Check the answer. Is $875 less than $29,550 equal to $28,675? \(29,550−875 \stackrel{?}{=}28,675\) \(28,675=28,675\) ✓
Step 7. Answer the question with a complete sentence.	The sticker price of the car was $29,550.

Table 2.2

Try It 2.23

Translate into an algebraic equation and solve:

Eddie paid $19,875 for his new car. This was $1,025 less than the sticker price. What was the sticker price of the car?

Try It 2.24

Translate into an algebraic equation and solve:

The admission price for the movies during the day is $7.75. This is $3.25 less the price at night. How much does the movie cost at night?