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Today: Review for Final Exam Mixture Type Problems
Alt.Khan here, due Friday Final Exam: Part I Wed., Part
II Thursday
June 9, 2014
1.
π±=Β±πβπ
Final Exam Review:
A rescue helicopter and an ambulance are both traveling from the scene of an accident to the hospital. Each grid line is 1 mile; the solid line represents the ambulance, the dotted line, the helicopter.
How far did each travel?
5x 1 3x 5 2.Set up the equationso that there will beonly one radical oneach side of the equal sign.
Square both sidesof the equation.
Simplify.
Simplify by dividingby a common factor of 2.
Square both sides of the equation.
5x 1 2 2 3x 5 2
5x 1
5x 1 3x 1 4 3x 5
2x 2 4 3x 5
x 1 2 3x 5
x 1 2 2 3x 5 2
x2 2x 1 4(3x 5) Use Foil.
5x 1 2 3x 5
Use Foil.4 4 3x 5 (3x 5)
Solve
Solving Radical Equations
x2 2x 1 4(3x 5) Distribute the 4.
x2 2x 1 12x 20 Simplify.
x2 10x 21 0 Factor the quadratic.
(x 3)(x 7) 0 Solve for x.
x - 3 = 0 or x - 7 = 0 x = 3 or x = 7 Verify both solutions.
5x 1 3x 5 2
5(3) 1 3(3) 5
4 2
2
5x 1 3x 5 2
5(7) 1 3(7) 5
6 4
2
Solving Radical Equations
L.S. R.S. L.S. R.S.
Rational Expressions vs. Equations
Rational Expressions Rational Equations
Word Problems:Mixture, Coin, Work,
Distance
Mixture Type Problems
A store mixes some candy worth $3.50 a pound with other candy costing $1.00/lb. There are 10 more pounds of the cheaper candy than the more expensive one. The total value of the mixture is $28. How many pounds of each type of candy are there? What is the per pound cost of the new candy mix?
Expensive
$3.50/ lb x lbs.
3.5x
Cheaper
$1.00/ lb x + 10
lbs.1(x + 10)
Mix
+ =
3.5x + 1.0x +10 = 28
x = 4; x + 10 = 14
$28
Mixture Type Word Problems:
Mixture Type Word Problems:
Redtop
$9.50/ lb 40 lbs. $9.50(40)
Mixture
$10.50/ lb 60 lbs. $10.50(60)
Bluegrass
x
100 lbs.
100x
$9.50(40) + $10.50(60) = 100x
x = $10.10
Gourmet
$8.00/ lb
10 lbs. $8.00(g)
$6.00/ lb
Regular
$6.75/ lb
g lbs. (10 - g) lbs. $6.00 (10 -
g)
Mixture
$6.75(10)
g = 3.75; r = 6.25
+ =
Class Work: See Handout
