- b.Let x= the number of nickels in the piggy
bank. Then there are 65 – xdimes in the bank.
The amount contributed to the total by the
nickels is 0.05xand the amount contributed by
the dimes is 0.10(65 – x). Since the total in the
bank is $5.00, we must solve the following
equation.
0.05x+ 0.10(65 – x) = 5.00The equation is solved as follows:0.05x+ 0.10(65 – x) = 5.00
0.05x+ 6.5 – 0.10x= 5.00
–0.05x= –1.5
x= –– 01 .. 055 = 30Thus, there are 30 nickels and 35 dimes in the
piggy bank.- b.Let x= Lisa’s current age (in years). Lori’s
age is 2x. The statement, “In 5 years, Lisa will
be the same age as her sister was 10 years ago”
can be expressed symbolically as the equation
x+ 5 = 2x– 10, which is solved as follows:
x+ 5 = 2x– 10
x= 15Thus, Lisa is currently 15 years old and Lori is
30 years old.Set 19 (Page 45)
- b.The fact that the graph of the line is solid
means that it is included in the solution set,
so the inequality describing the shaded region
must include equality (that is, it must be either
or ). Next, since the shaded region is below
the horizontal line y= –2, all points in the solu-
tion set have a y-value that is less than or equal
to –2. Hence, the inequality illustrated by this
graph is y – 2.
290. a.The graph of the line is solid, so it is
included in the solution set and the inequality
describing the shaded region must include
equality (either or ). Next, since the graph
of the line rises from left to right at the rate of
two vertical units up per one horizontal unit
right, its slope is 2. And, since it crosses the y-
axis at (0,7), we conclude that the equation of
the line is y= 2x+ 7. Finally, since the shaded
region is below the liney= 2x+ 7, the inequal-
ity illustrated by this graph isy
2 x+ 7. This
can be verified by choosing a point in the
shaded region, say (0,0), and observing that
substituting it into the inequality results in the
true statement 0 7. - b.The graph of the line is dashed, so it is not
included in the solution set and the inequality
describing the shaded region must not include
equality (it must be eitheror). Next, since
the graph of the line falls from left to right at the
rate of four vertical units down per one horizon-
tal unit right, its slope is –4. Since it crosses the
y-axis at (0,–3), we conclude that the equation of
the line is y= –4x – 3. Finally, the shaded region
is below the liney= –4x – 3, so we conclude that
the inequality illustrated by this graph isy
–4x – 3. This can be verified by choosing any
point in the shaded region, say (0,–4), and
observing that substituting it into the inequality
results in the true statement –4–3.
292. c.The graph of the line is dashed, so it is not
included in the solution set and the inequality
describing the shaded region must not include
equality (it must be eitheror). Next,
since the shaded region is to the left of the ver-
tical line x = 8, all points in the solution set
have an x-value that is less than or equal to 8.
Hence, the inequality illustrated by this graph
is x 8.
ANSWERS & EXPLANATIONS–