Transcript Solving Proportions Power Point

WRITING AND SOLVING PROPORTIONS

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Sports A person burned about 150 calories while
skateboarding for 30 minutes. About how many calories would
the person burn while skateboarding for 60 minutes? In
Example 1, you will use a proportion to answer this question.
A proportion is an equation that states that two ratios are
equivalent.
Algebra =
, where b and d are nonzero numbers.
EXAMPLE 1 USING EQUIVALENT RATIOS

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Sports A person burned about 150 calories while
skateboarding for 30 minutes. About how many
calories would the person burn while
skateboarding for 60 minutes? In Example 1, you
will use a proportion to answer this question.
To find the number C of calories the person
would burn while skateboarding for 60 minutes,
solve the proportion = .
Answer: Ask yourself, what number can you multiply
by 30 to get 60? The answer is 2. So, multiply 150 x
2 to get 300. So the person would burn about 300
calories while skateboarding for 60 minutes.
EXAMPLE 2 SOLVING PROPORTIONS USING
ALGEBRA
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Solve the proportion =
.
EXAMPLE 2 WRITING AND SOLVING A
PROPORTION
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Setting Up a Proportion There are different
ways to set up a proportion. Consider the
following problem.
Yesterday you bought 8 bagels for $4. Today
you want only 5 bagels. How much will 5
bagels cost?
WRITING AND SOLVING A PROPORTION
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Empire State Building
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Step 1: Write a proportion:
At maximum speed,
the elevators in the Empire State Building
can pass 80 floors in 45 seconds. Follow the
steps below to find the number of floors
that the elevators can pass in 9 seconds.
𝑓𝑙𝑜𝑜𝑟𝑠
80 𝑥
=
=
𝑠𝑒𝑐𝑜𝑛𝑑𝑠 45 9
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Step 2: Solve the proportion:
9∙
80
45
720
45
𝑥
9
= ∙9
multiply both sides by 9
=𝑥
divide 720 by 45
16 = x
LESSON 5: SOLVING PROPORTIONS USING
CROSS PRODUCTS
In the Real World
 Science At space camp, you can sit in a
chair that simulates the force of gravity on
the moon. A person who weighs 105 pounds
on Earth would weigh 17.5 pounds on the
moon. How much would a 60 pound dog
weigh on the moon? You’ll find the answer
in Example 2.
In the proportion , the products 2 • 6 and 3 • 4
are called cross products. Notice that the
cross products are equal. This suggests the
following property.
CROSS PRODUCTS PROPERTY
Cross Products Property
Words The cross products of a proportion are equal.
EXAMPLE 1 SOLVING A PROPORTION
USING CROSS PRODUCTS
Use the cross products property to solve.
EXAMPLE 2 WRITING AND SOLVING A
PROPORTION

Science At space camp, you can sit in a
chair that simulates the force of gravity on
the moon. A person who weighs 105 pounds
on Earth would weigh 17.5 pounds on the
moon. How much would a 60 pound dog
weigh on the moon?
EXAMPLE 3 WRITING AND SOLVING A
PROPORTION
Penguins At an aquarium, the ratio of
rockhopper penguins to African penguins is
3 to 7. If there are 50 penguins, how many
are rockhoppers?
 First, determine the ratio of rockhoppers to
total penguins. Then, set up proportion.
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YOUR TURN
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In John’s class, the ratio of boys to girls is 5
to 8. If there are 39 students in his class,
how many are girls?