SECTION 2.7 Further Applications of Linear Equations^143
Step 3 Write an equation.Multiplying the number of bills by the denomination
gives the monetary value. The value of the tens added to the value of the
fives must be $200.
Value of value of
tens plus fives is $200.10 x 200
Step 4 Solve. Distributive property
Combine like terms.
Subtract 125.
Divide by 15.Step 5 State the answer.The teller has 5 tens and fives.
Step 6 Check.The teller has more fives than tens. The value of the
money is
51 $10 2 + 301 $5 2 =$200, as required. NOW TRY
30 - 5 = 25
5 + 25 = 30
x= 5
15 x= 75
15 x+ 125 = 200
10 x+ 5 x+ 125 = 200
+ 51 x+ 252 =
NOW TRY
EXERCISE 4
Clayton has saved $5.65 in
dimes and quarters. He has
10 more quarters than dimes.
How many of each denomina-
tion of coin does he have?
Distance, Rate, and Time Relationshipt
d
r
r
d
t
drt
Finding Distance, Rate, or TimeSolve each problem using a form of the distance formula.
(a)The speed of sound is 1088 ft per sec at sea level at 32°F. Find the distance sound
travels in 5 sec under these conditions.
We must find distance, given rate and time, using
1088 5 5440 ft
Rate Time Distance(b)The winner of the first Indianapolis 500 race (in 1911) was Ray Harroun, driving
a Marmon Wasp at an average rate (speed) of 74.59 mph. (Source: Universal
Almanac.) How long did it take him to complete the 500 mi?
We must find time, given rate and distance, using
(rounded) Time
500
74.59
=6.70 hr
Aor
dt= r =tB.
d
r^* =* =
d=rt 1 orrt=d 2.
EXAMPLE 5
Distance
RateTo convert 0.70 hr to minutes, we multiply by 60 to get It took
Harroun about 6 hr, 42 min, to complete the race.
0.70 1602 =42.
OBJECTIVE 5 Solve problems involving distance, rate, and time. If your
car travels at an average rate of 50 mph for 2 hr, then it travels
This is an example of the basic relationship between distance, rate, and time,
given by the formula By solving, in turn, for rand tin the formula, we obtain
two other equivalent forms of the formula. The three forms are given here.
d= rt.
distancerate:time,
50 * 2 =100 mi.
NOW TRY ANSWER
- dimes: 9; quarters: 19