1.
Find the equation
of the line in slope intercept form that passes through (3, -2) and (5, 1).
a.
Find the slope of
the line:
3/2
b.
Find the
y-intercept:
Y =
mx + b
1 =
3/2 (5) + b
1 =
15/2 + b
-13/2 = b
c.
The equation of
the line is:
Y =
3/2 x 13/2
2.
Find the equation
of the vertical line passing through (5, 7).
So
in this case it is x = 5
3.
Graph the line
3x=7.
Solve
for x;
X =
7/3. This is a vertical line through
(7/3, 0)
4.
Find the equation
of the horizontal line passing through (2, 4).
So
in this case it is y = 4.
5.
Find the equation
of the line parallel to 3x -5y = 7 passing through the point (5, 1).
a.
In this case we
have a point. We need the slope. Since the line is parallel to 3x -5y = 7 it
will have the same slope. Find the slope
by solving for y.
-5y
= -3x + 7
y =
3/5 x 7/5
The
slope is 3/5.
b.
Find b.
Y =
mx + b
1 =
3/5(5) + b
1 =
3 + b
b =
-2
c.
The equation of
the line is:
Y =
3/5 x 2
6.
In 1990 the
X =
the year from 1990
Y =
the
Points:
(0, 248.7) and (10, 281.4)
M =
3.27
B =
248.7
Y =
3.27x + 248.7
In
2004, x = 14
Y =
3.27(14) + 248.7
Y =
45.78 + 248.7
Y =
294.48 million people in 2004
340
= 3.27 x + 248.7 and solve.
X is about the year 2017 or 2018.
7.
The value of a
set of 35 dimes and nickels is worth $2.75.
How many of each coin do you have?
|
|
Amount |
Value/ coin |
Total value |
|
Nickels |
x |
5 |
5x |
|
Dimes |
35 x |
10 |
10(35 x) |
5x + 10(35 x) = 275
5x + 350 -10x = 275
-5x = -75
x = 15
There are 15 nickels and 20 dimes in the collection.
8.
Coach Leslie
heads for
|
|
Rate |
Time |
Distance |
|
Leslie |
62 |
x |
62 x |
|
Soffa |
71 |
X - 3 |
71(x 3) |
X = number of hours that Coach Leslie drove.
62x = 71(x 3)
62x = 71x 213
-9x = -213
x = 23 2/3 hours
Captain Soffa catches up to coach Leslie ant
the next
morning.
9.
Mark, the
chemist, mixes 5ml of a 75% acid solution with a 42% acid solution. How many milliliters of the 42% solution does
he need to create a 60% acid solution?
|
|
Amount |
Rate (%) |
Amount of Pure Acid |
|
Soln 1 |
5 |
.75 |
3.75 |
|
Soln 2 |
X |
.42 |
.42x |
|
Mix |
X + 5 |
.60 |
.6(x + 5) |
X =
amount of 42% solution
3.75
+ .42x = .6(x + 5)
3.75
+ .42x = .6x + 3
.75
= .18x
x =
4 1/6 ml of the 42% solution.
10.
A five quart
radiator has a 45% antifreeze solution in it.
Some of this is drained and replaced with pure antifreeze to create a
55% antifreeze solution. How many quarts
were drained and then replaced with pure antifreeze? (Very difficult)
|
|
Amount |
Rate (% antifreeze) |
Amount of pure antifreeze |
|
Left in the radiator |
5 - x |
.45 |
.45(5 x) |
|
Pure antifreeze added |
X |
1.00 |
X |
|
Final solution |
5 |
.55 |
2.75 |
X =
the amount drained from the radiator and replaced with pure antifreeze.
.45(5
x) + x = 2.75
2.25
-.45x + x = 2.75
.55x
= .5
x =
10/11 or .9090
quarts need to be drained and then replaced with pure
antifreeze in order to increase the level in the radiator to a 55% solution.
11.
Laure invests $20,000 into three accounts, stocks, bonds
and foreign investments. She has $2,000
less than three times the amount she invested in the foreign market in
bonds. The stocks earned an interest
rate of 4%, the bonds 3% and the foreign accounts 5%. The return on her account after one year was
$740, how much was invested in bonds?
|
|
Principal |
Rate |
Interest |
|
Stocks |
|
.04 |
|
|
Bonds |
3x 2000 |
.03 |
|
|
Foreign |
X |
.05 |
|
X =
the amount invested in the foreign accounts.
The
problem is finding the principal invested in stocks. However, we know the total amount invested
was $20,000 and the amount invested in bonds and the foreign was 4x 2000.
So
the principal in stocks was:
20000
(4x -2000)
or
22000 4x
|
|
Principal |
Rate |
Interest |
|
Stocks |
22000 4x |
.04 |
.04(22000 4x) |
|
Bonds |
3x 2000 |
.03 |
.03(3x 2000) |
|
Foreign |
X |
.05 |
.05x |
.04(22000
4x) + .03(3x 2000) + 05x = 740.
880
- .16x + .09x 60 + .05x = 740
-.02x
= - 80
x =
$4000
There
was $10,000 invested in bonds.
12.
Solve for a
variable explicitly.
13.
Proportion
problems