Transcript Solve

Problem Solving
Using Ratios and
Proportions
Ratio: same units written as a
fraction where a and b are
non-zero numbers.
a
b
a:b
a to b
Proportions: two ratios set
equal to each other.
a c

b d
b d

a c
Where a,b,c, and d
are non-zero
numbers
Reciprocals are
equal
Cross products are
ad=bc always equal!
Clears away
fraction!
Left with an equation
to solve!
Solve:
3 5

y 8
5y=24
24
y
5
Divide
both
sides
by 5
x
2

x4 x
2
x =2(x+4)
2
x =2x+8
Move 2x and 8 to keep
positive!
2
x
2
x -2x-8=0
(x-4)(x+2)=0
Factor to get
solutions
(x-4)= 0 or (x+2)=0
x=4 and x=-2
Proportions or similar
shapes:
set up proportions with
corresponding sides and
solve for the unknown.
If a flag pole is 15 feet high and
casts an 8 foot shadow, how tall is a
tree that casts an 11 foot shadow?
15ft.
? ft.
11ft.
8ft.
Set up proportion and solve:
• Shadow tree = shadow flagpole
actual tree actual flag pole
11
x
=
8
15
8x = 165
x = 20.62 ft.
Cross multiply
Solve for x