Beginning Algebra, 11th Edition

Step 3 Write two equations.The total distance traveled by both cars is 400 mi,

which gives the first equation.

The faster car goes 20 mph faster than the slower car, which gives the

second equation.

Step 4 Solvethe system of equations.

(1)

(2)

Use substitution. Replace xwith in equation (1) and solve for y.

(1)

Let

Distributive property

Combine like terms.

Subtract 80.

Divide by 8.

Then

Step 5 State the answer.The rates of the two cars are 40 mph and 60 mph.

Step 6 Check.Since each car travels for 4 hr, the total distance traveled is

mi, as required.

NOW TRY

41602 + 41402 = 240 + 160 = 400

x= 20 +y= 20 + 40 =60.

y= 40

8 y= 320

80 + 8 y= 400

80 + 4 y+ 4 y= 400

4120 +y 2 + 4 y= 400 x= 20 +y.

4 x+ 4 y= 400

20 + y

x= 20 +y

4 x+ 4 y= 400

x= 20 + y

4 x+ 4 y= 400

276 CHAPTER 4 Systems of Linear Equations and Inequalities

NOW TRY
EXERCISE 4
From a truck stop, two trucks
travel in opposite directions on
a straight highway. In 3 hr they
are 405 mi apart. Find the rate
of each truck if one travels
5 mph faster than the other.

NOW TRY ANSWER

4. faster truck: 70 mph;
   slower truck: 65 mph

Distribute 4 to

both20 and y.

Complete solution available
on the Video Resources on DVD

4.4 EXERCISES

Concept Check Choose the correct response in Exercises 1–7.

1.Which expression represents the monetary value of x5-dollar bills?

A. dollars B. dollars C. dollars D. 5 xdollars

2.Which expression represents the cost of tpounds of candy that sells for $4.95 per lb?

A.$4.95t B. C. D.

3.Which expression represents the amount of interest earned on ddollars at an interest rate

of 3%?

A. 3 ddollars B.0.03ddollars C.0.3ddollars D. 300 ddollars

4.Suppose that Ira Spector wants to mix xliters of a 40% acid solution with yliters of a

35% solution to obtain 100 L of a 38% solution. One equation in a system for solving this

problem is. Which one of the following is the other equation?

A. B.

C. 35 x+ 40 y= 38 D. 40 x+ 35 y=0.38 11002

0.35x+0.40y=0.38 11002 0.40x+0.35y=0.38 11002

x+y= 100

$4.95+t

t

$4.95

$4.95

t

15 +x 2

5

x

x

5

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