Warm Up

#1

#2

The system below has a solution of (2,1). Find the values of a and b.

ax by 4

bx ay 10

At Randy’s bike shop, they only work on bicycles and tricycles. When Randy disassembled all the bikes and trikes he ended up with 34 seats and 89 wheels. How many tricycles does he have in his shop?

Warm Up

#1 The system below has a solution of (2,1). Find the values of a and b.

ax by 4

bx ay 10

2a b 4

2b a 10

2a b 4

a 2b 10

2a b 4

2a 4b 20

3b 24b 8a 6

Warm Up

#2 At Randy’s bike shop, they only work on bicycles and tricycles. When Randy disassembled all the bikes and trikes he ended up with 34 seats and 89 wheels. How many tricycles does he have in his shop?

b number of bicycles

t number of tricycles

b t 34 2b 3t 89

21 tricycles

2b 2t 68

t 21

2b 3t 89

Define variables: Write two equations

E1

E2

Word Problems

Homework

With a tailwind, a helicopter flies 270 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?

Withthe wind

270

Rate Time Distance

Againstthe wind

1.5h w h w 1.5 270

h w 3 270 2703h w

w = speed of wind (mph) h = speed of the helicopter (mph)

#1

Homework

#1 With a tailwind, a helicopter flies 270 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?

h w 1.5 270

h w 3 270

w = speed of wind (mph) h = speed of the helicopter (mph)

h w 180

h w 90 2h 270h 135w 45

Wind = 45 mph

Homework

#2 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.

Withthe current

24

Rate Time Distance

Againstthe current

2b c b c 2 24

b c 3 24 243b c

b = speed of barge (mph) c = speed of the current (mph)

Homework

b c 12

b c 8

2b 20b 10c 2

barge = 10 mph

current = 2 mph

#2 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.

b = speed of barge (mph) c = speed of the current (mph)

b c 2 24

b c 3 24

Homework

Bubba has a collection of 95 coins, consisting of only nickels, dimes and quarters. If the number of quarters and dimes combined is 60, and the total value of all his coins is $12.70, how many dimes does he have?

d = number of dimesq = number of quarters

Define variables:

d q 60 Write two equations

E1

E2

Number of nickels = 35

Value of nickels = $1.75

Value of dimes and quarters = $10.95

25d 25q 1500

15d 405 d 27

27 dimes

#3

10d 25q 1095

Homework

#4 The length of a rectangle is three more than it’s width. If the perimeter is 66 meters, find the area of the rectangle.

L = length

W = width

Define variables: Write two equations

E1

E2

L W 3 2L 2W 66

2 2 63 6W W E1 E2

2W 6 2W 66 4W 60W 15L 18

2Area 270 m

L

WArea?

Weekly WorkoutIn a math contest, each team is asked 50 questions. The teams earn 15 points for every correct answer and lose 8 points for every incorrect answer. Team A won the contest and scored 566 points. Team B finished second and missed 4 more questions than team A. How many questions did team B get correct?

#1

c = correct answers

w = wrong answers

Define variables:

c w 50

Write two equations

E1

E2 15c 8w 566 8c + 8w=40015c 8w 566

23c =966

c =42Team B: 38 correct

Weekly Workout#2 Ally has $30 more than Carl. If they each had $7 less, the sum of their

money would be equal to what Ally has now. How much money does Carl have?

a = Ally’s money

c = Carl’s money

Define variables:

a c 30

Write two equations

E1

E2 (a −7) (c −7) aa c 14 a

c 14 0

c 14Carl: $14

Weekly Workout#3 If 1 is subtracted from the numerator of a fraction, the resulting fraction is

1/3. If 2 is subtracted from the denominator , the resulting fraction is 1/2. Find the original fraction.

3n 3 d n = Numerator

d = Denominator

Define variables: Write two equations

E1

E2

nd

13

3 n 1 d

n 1d

3n 3 d

Weekly Workout#3 If 1 is subtracted from the numerator of a fraction, the resulting fraction is

1/3. If 2 is subtracted from the denominator , the resulting fraction is 1/2. Find the original fraction.

3n 3 d n = Numerator

d = Denominator

Define variables: Write two equations

E1

E2

nd

nd 2

12

2n d 2 2n 2 d

d d

3n 3 2n 2 n 5d 12

512

2n 2 d

Weekly Workout#4 A jar containing only nickels and quarters totals $5.60. There are

half as many quarters as there are nickels. How many nickels are in the jar?

n = number of nickels

q = number of quarters

Define variables:

n 2qWrite two equations

E1

E2 5n 25q 560

E1 E2

5 25 62q q 5 0 35q 560

q 16

32 nickels n=q n=2q

Weekly Workout#5 A chemist makes 10 liters of a 30% acid solution by mixing a 20% acid

solution with a 50% acid solution. Find exactly how many liters of the 20% solution that he used.

a = amount of 20% acid solution

b = amount of 50% acid solution 0.30(10) = 3

Amount of Solution

acid

a b 10

0.20a 0.50b 3

+ =20%solution

50%solution

30%solution

a b 10

0.20a 0.50b 3

Weekly Workout#5 A chemist makes 10 liters of a 30% acid solution by mixing a 20% acid

solution with a 50% acid solution. Find exactly how many liters of the 20% solution that he used.

a = amount of 20% acid solution

b = amount of 50% acid solution

a b 10

0.20a 0.50b 3 2a 5b 30

5a 5b 50

3a 20 20

a3

26 liters of 20% solution

3

Weekly Workout#6 The length of a rectangle A is 3 less than twice its width and it has a

perimeter of 54 meters. Rectangle B has dimensions that are exactly twice that of rectangle A. Find the area of rectangle B.

L = Length (A)

W = Width (A)

Define variables:

A

L 2W 3

Write two equations

E1

E2 2L 2W 54

B2680 mFind the area of rectangle B

L

W

52W 432 2W E1 E2

4W 6 2W 54

6W 60W 10L 17

2L

2W20

34

Weekly Workout