The document contains several math word problems and examples involving ratios, proportions, unit rates, and scale drawings. It includes problems finding the lengths of pieces of rope cut into sections, the number of bones in human ears and skulls given a ratio, the number of games lost by a baseball team based on their win-loss ratio, and examples of setting up and solving proportions.

1. January 14, 2016

2. x = 9, x1 = 11, x2 = 16
1. A 36 foot rope is cut into three pieces. The first
piece is 5 feet shorter than the longest, while the
other piece is 2 feet shorter than the first. How long
is each piece?
P = 43
The dimensions of a triangle are shown.
What are the lengths of each side of the
triangle?

3. Find the solution(s) to the following:

4. Write the number nine as a fraction with a denominator of four.
The reciprocal of
𝟏
𝟓
divided by The reciprocal of 5 =
(The opposite of -
𝟐
𝟑
) – (The opposite and reciprocal of - 6) =

7. 𝟐
𝟑
:
𝟏
𝟑
Simplify the folowing ratios:
3 :
𝟏
𝟐
3
𝟏
𝟐
: 8 Try simplifying
these ratios:

8. The ratio of the number of bones in a human’s ears to the
number of bones in the skull is 3:11. There are 22 bones in
the skull. How many bones are in the ears?
Write a ratio comparing bones in ears
to bones in skull.
Write a proportion. Let x be the
number of bones in ears.
Since x is divided by 22, multiply
both sides of the equation by 22.
There are 6 bones in the ears.

9. The ratio of games lost to games won for a baseball team
is 2:3. The team has won 18 games. How many games did
the team lose?
The team lost 12 games.
Write a ratio comparing games lost to games won.
Write a proportion. Let x be the number of games lost.
Since x is divided by 18, multiply
both sides of the equation by 18.

10. The ratio of games lost to games won for a baseball team
is 2:3. The team has played 45 games. How many games
did the team lose?
Write a ratio comparing games lost to total games
Write a proportion. Let x be the number of games lost.

11. 1. Chas and Dave share 60 Magic Wizard Cards in a 2:3
ratio. How many cards does each receive?
2. $1225 is shared in a 3:4 ratio. How much does each
person receive? (Be careful when setting up proportion)
3. The ratio of Freshmen to Seniors at MHS has been
right around 5:3 for a number of years. If there are 510
freshmen, how many can we expect to graduate?
Chaz, 24 & Dave, 36
Person 1: $525 Person 2: $700
306
3
7
=
x_
1225
5
3
=
510
x

12. 1. A 64 oz. Apple Juice costs $1.35. Find the unit rate.
2. A 12 slice pizza costs $9.00. Find the unit rate.
3. A pipe leaks 40 gallons of water every hour.
How long does it take to leak one gallon?
Which unit, (oz. or $) do we want to reduce to 1?

14. Unit rate: 30 miles,
1 hour
or 30 mi/(1)h
The ratio 90
3
can be simplified by dividing:
90
3
= 30
1
A driver travels 90 miles in 3 hours. What is the
unit rate?

15. 𝒅𝒓𝒂𝒘𝒊𝒏𝒈 (𝒊𝒏. )
𝒂𝒄𝒕𝒖𝒂𝒍 (𝒇𝒕. )
Scale
1 in. = 2.5 ft. Set up your proportions first
Length Height
𝟏
𝟐.𝟓
=
𝟒
𝒙
𝟏
𝟐.𝟓
=
𝟏.𝟐𝟓
𝒙