Beginning Algebra, 11th Edition

SECTION 2.4 An Introduction to Applications of Linear Equations^111

Analyzing a Gasoline-Oil Mixture

A lawn trimmer uses a mixture of gasoline and oil. The mixture contains 16 oz of

gasoline for each 1 ounce of oil. If the tank holds 68 oz of the mixture, how many

ounces of oil and how many ounces of gasoline does it require when it is full?

Step 1 Readthe problem. We must find how many ounces of oil and gasoline are

needed to fill the tank.

Step 2 Assign a variable.

Let

Then

A diagram like the following is sometimes helpful.

16 x= the number of ounces of gasoline required.

x=the number of ounces of oil required.

NOW TRY EXAMPLE 4

EXERCISE 4
At the Sherwood Estates pool
party, each resident brought
four guests. If a total of 175
people visited the pool that
day, how many were residents
and how many were guests?

Oil

x

Gasoline

16 x

Tank

5 68

Sometimes we must find three unknown quantities. When the three unknowns are

compared in pairs,let the variable represent the unknown found in both pairs.

PROBLEM-SOLVING HINT

Step 3 Write an equation.

Amount of amount total amount

gasoline plus of oil is in tank.

16 xx 68

Step 4 Solve. Combine like terms.

Divide by 17.

Step 5 State the answer.The lawn trimmer requires 4 oz of oil, and

of gasoline when full.

Step 6 Check.Since and 64 is 16 times 4, the answer checks.

NOW TRY

4 + 64 =68,

16142 = 64 oz

x= 4

17 x

17

=

68

17

17 x= 68

+ =

Dividing a Board into Pieces

A project calls for three pieces of wood. The longest piece must be twice the length

of the middle-sized piece. The shortest piece must be 10 in. shorter than the middle-

sized piece. If a board 70 in. long is to be used, how long can each piece be?

Step 1 Readthe problem. There will be three answers.

Step 2 Assign a variable.Since the middle-sized piece appears in both pairs of

comparisons, let xrepresent the length, in inches, of the middle-sized piece.

Let

Then

and x- 10 =the length of the shortest piece.

2 x=the length of the longest piece,

x=the length of the middle-sized piece.

EXAMPLE 5

NOW TRY ANSWER

4. 35 residents; 140 guests