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Mixed Linear Algebra Problems

Linear equations:

A) 3x - 5(6 - 2x) = 4(x - 8) + 3

B) (w - 3)/8 - (5 - w)/4 = (4w - 1)/8 - 1

C) a = 1 /2(b1 + b2)

For each formula express y as a function of x:

D) y -3 = 1 / 3(x-4)

Solve for the specified variable:

E) xy + 5 = x + 7 for x

Solve the equation. Round answers to three decimal places:

F) 457(36x - 99) = 32(28x - 239)

Find y given that x = 3:

G) y = -3x - 6

Find x given that y = 2, z = -3, and w = 4:

H) z(x - y) = y(x + 5)

Finding the time:

I) If the simple interest on $10,000 at 6% is $3000 then what is the time?

Cigarette usage:

J) The percentage of Americans 18 to 25 who use cigarettes has been decreasing at an approx constant rate since 1974. The function:
P = 47.9 - 0.94n
i) use the formula to find the percentage of smokers in this age group in 2006
ii) use the accompanying graph to estimate the year in which smoking will be eliminated from this age group
iii) use the formula to find the year in which smoking will be eliminated from this age group

Show a complete solution for each number problem:

K) Four consecutive odd integers have a sum of 56. What are the integers?

L) Isoceles triangle. A flag in the shape on an isoceles triangle has a base that is 3.5 inches shorter than either of the equal sides. If the perimeter of the triangle is 49 inches what is the length of the equal sides?

Mixture problems:

M) Alcohol solutions. How many liters of a 10% alcohol solution should be mixed with 12 liters of a 20% alcohol solution to obtain a 14% alcohol solution?

Uniform motion problems:

N) Walk, dont run. Louise walked for 2 hours than ran for 1 and 1/2 hours. If she runs twice as fast as she walks and the total trip was 20 miles then how fast does she run?

Solution Preview

See the attached file for solutions.

#76 3x - 5(6 - 2x) = 4(x - 8) + 3
3x -30 +10x = 4x -32 + 3
13x -30 = 4x - 29
13x - 4x = -29 + 30 = 1
9x = 1
X = 1 /9

#100 (w - 3)/8 - (5 - w)/4 = (4w - 1)/8 - 1 (The question format is not clear, so I'm assuming it's this)
(w-3) / 8 - (5-w)2 /8 = (4w-1)/8 - 8/8
(w-3 -10 + 2w) / 8 = (4w - 1 - 8) /8
3w - 13 = 4w - 9
3w - 4w = -9 + 13 = 4
W = -4

#14 a = 1 /2(b1 + b2) (Assuming b1 + b2 is part of the denominator)
B1 + b2 = 1 / 2a
B2 =( 1/2a) - b1
B2 = (1 - 2ab1) / 2a

#26 y -3 = 1 / 3(x-4)
Y = 1 / 3(x-4) + 3
Y = (1 + 9x - 36) / (3x -4)
Y = (9x - 35) / (3x -4)

#32 xy + 5 = x + 7 for x
Xy - x = 7 - 5 = 2
X( y -1) = 2
X = ...

Solution Summary

Mixed linear algebra problems are examined.

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