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LiteralEquations

Unit RatesProblem solving

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Dimensional analysis

Percent ofChange

Find the percent of change

original weight: 21.8 grams

New weight: 36.4 grams

Write answer to nearest tenth.

67.0% increase

How much would you pay for an item with an original price of $68, if you have a coupon

for 30% off and 8% sales tax?

$51.41

What was the original price of an item if you paid $10.66 including a tax of 6.75%?

$9.99

The current price of each share of a technology company is $135.

This is a 16.2% increase over the past year. What was the price a

year ago?

$116.18

On Monday, Sammy the storekeeper decides to increase the price of avocados by 20%. On Tuesday, he increases this price by another 25%.

a. What percent of the original avocado price is the price of avocados after both increases?

b. On Wednesday, Sammy returned the avocados to their original price,

a. 150% increase b. 33⅓% decrease

Solve

2a + 2b = c for b

What are the restrictions?

Solve x/5 - g = a for x

What are the restrictions?

x = 5(a + g)

There are no restrictions since no variable is in the 

denominator

Solve 9 + 3x = 2y    for xWhat are the restrictions?

X = ⅔y -3

There are no restrictions since no variable is in the 

denominator

Solve :  y = mx + b for m. 

What are the restrictions?What can you say about y if m = 0?

Convert 

9000 seconds to hours

(using dimensional analysis)

 Use dimensional analysis to convert 3.5 km to cm

Use dimensional analysis to convert 

25 miles per hour into 

feet per second

Use dimensional analysis to convert

3 feet/ sec. to miles per hour.

Use dimensional analysis to convert

2 gallons/ sec. to quarts/ min.

Define Unit Rate

A rate with 1 in the denominator or a rate

comparing to a single unit

A car traveling 36 ft./sec would travel how many

miles/hour?

(use dimensional analysis)

Give two possible unit rates for 8 cans for $16.

If 3 Marios = 4 Luigis

2 Luigis = 5 Yoshi

Convert 40 Yoshi to Marios

Use dimensional analysis

If a woodchuck could chuck wood:

5 wood chucks chucked 5 pieces of wood in one

hour.

How much wood could one wood chuck chuck

in 3 hours?

3 pieces of wood

Find the number of round-trip commuter rail tickets sold.

1.Thirty times as many round trip tickets as 12-ride tickets were sold.

2. The total number of tickets sold represented 1440 rides.

Rides per x ticket

Number of tickets sold

= total rides

12-ride tickets ? N ?

Round-trip ticket

? ? ?

12n + 60n = 1440

72n=1440

n = 20

Therefore, there were 20 12-ride tickets and

There were 60 round trip commuter rail tickets sold.

Rides per x ticket

Number of tickets sold

= total rides

12-ride tickets 12 n 12n

Round-trip ticket

2 30n 60n

Find the total amount of time Joel spent watching space adventure movies.

1.He saw twice as many 1.5 hour movies as he did 2 hour movies.

2.He spent a total of 15 hours watching movies.

Movie length x

# of movies = Total time

Space movies ? ? ?

Mystery movies

? ? ?

The length of a rectangle is twice its width, w. A second rectangle, which is 8 cm longer and 3 cm narrower than the first rectangle, has the perimeter 154 cm. Make a sketch of the rectangles, expressing all dimensions in terms of w. Then find the dimensions of each rectangle.

Use 5 step plan.

Movie length x

# of movies = Total time

Space movies

1.5 2m 1.5(2m)

Mystery movies

2 m 2m

Step 2: Let m = number of mystery movies (since it is smaller amount). Step 3: We know that the total time is 15 hours for watching all movies.Length of space movie (# of space movies) + length of mystery(# of mystery movies) = 15 hours(1.5)2m + 2m = 15 hours3m + 2m = 15 hours5m = 15 hoursm= 3 Therefore, 2m = 6 .

Total time watching space movies = 1.5(2)(3)= 9 hours.Check: (1.5)2(3) + 2(3) = 15 9 + 6 = 15

Step 1: Given info in chart: Question is find the amount of time Joel spent watching space movies.

w-38 + 2w w

2wStep 1: Given info in diagram. We also know the perimeter if yellow rectangle is 154 cm. Step 2: let w = width of first rectangle since it is smaller. Step 3: Perimeter of yellow rect. Step 4:2(8 + 2w) + 2(w-3) = 154; solve for w. 16 + 4w + 2w – 6 = 154 6w + 10 = 154 6w =144 w= 24 Step 5: Therefore the dimensions of the red rectangle are 24 x 48 cm, and the other rectangle are: 21 x 56.Check: 2 (24-3) + 2(8 + 2(24)) = 1542(21) + 2(56)= 154

rect. Width Length Perim.

Red w 2w

Yellow w -3 8 + 2w

2(w-3) + 2(8+2w)

Mona earns three times as much as an actuary as she does a writer.

Her total income is $40,000 more than that of her brother.

He earns half as much as Mona does as an actuary.

What is Mona’s salary as an actuary?

Use 5 step plan and chart to help.

Step 1: is listed in chart. Question: what is salary as an actuary?

Step2: let n = salary as a writer (since she earns less as a writer, it is easier to let the variable represent the smaller amount.

See the chart for other variables.

Step 3:

Her total income is $40, 000 more than her brother.

n + 3n = $40,000 + 1.5n

4n = 40,000 + 1.5n

2.5n = 40,000

n= 16, 000

Therefore, Mona earns 3(16,000)= $48,000 as an actuary.

Check: $16,000+$48,000= 40,000 + (1.5)(16,000)

Mona’s salary as writer n

Mona;s salary as actuary 3n

Brother’s salary 1.5n

Leo’s garden which is 6m wide, has the same area as Jen’s garden, which is 8 m

wide.

Find the lengths of the two rectangular gardens if Leo’s garden is 3 m longer than

Joe’s garden.

Make a sketch to help. Use five step plan.

LEO’s Garden Jen’s garden

6 meters

8 meters

L + 3

L

Length x width = Area

Leo’s garden L + 3 6 6(L + 3)

Jen’s garden L 8 8L

Step 1: Given information above and both gardens have SAME area: what are the lengths of each garden?Step 2: Let L = length of Jen’s garden (since it is smaller)Step 3: A= Length x widthArea of Leo’s garden = area of Jen’s garden6(L+3) = 8L6L + 18 = 8L18 = 2LL = 9: L+ 3 = 12 Therefore, Leo’s garden is 12 m long, and Jen’s is 9 meters long.Check: 6(12) = 8 (9)

Make your wager

In one basketball game, Maria scored three times as many points as Holly. In the next game, Maria scored 7 fewer

points than she did in the first game, while Holly scored 9 more points than she did in the first game. If they scored the same number of points in the second game, how many

points did each score in the first game?

Game 1 Game 2

Holly h h + 9

Maria 3h 3h -7

Step 1: Given info in above chart: we know both Holly and Maria scored same amount of points in Game 2. The question: how many points did each score in game 1?Step 2: let h = number of points holly scored in game 1 (since this is smaller amount).Step 3: since we know they scored the same amount of points in game 2, we can say: h + 9 = 3h – 7 and solve for h (Holly’s points for game 1).Step4: -h +7 = -h + 7

16 = 2h, h = 8Step 5: Holly scored 8 points in game 1 and Maria scored 24 points.Check: 8 + 9 = 3(8) – 7

17 = 17 (they both scored 17 points in game 2)