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# Mixture Project

Period 5
Anthony Lopez,Joseph Nguyen, Bao Le, Eliseo Canela, Vincent Nguyen

by

Tweet## Anthony Lopez

on 14 December 2012#### Transcript of Mixture Project

Per.5

By:Anthony Lopez

Joseph Nguyen

Bao Le

Eliseo Canela

Vincent Nguyen The Mixture Problems In our presentation, we

will present you 10 question

about mixture problems

that we have covered in class. Question 1: A special tea blend is made from two varieties of herbal tea,

one that cost $4.00/lb and another that cost $2.00/lb. How many pounds of each type are needed to make 20 pounds of a blend worth $2.50/lb? Define the variables:

x= pounds of the $2.00 herbal tea

y= pounds of the $4.00 herbal tea Lets begin doing the problems The Work

x+y=20

2x+4y=20(2.5)

2x+4y=50

2(x+y=20)

2x+4y=50

2x+2y=40

- - -

2x+4y=50

-2y=-10

/-2 /-2

y=5 We choose

elimination

because

the equations

are lined up. And now we subtract Since there are only 20 pounds of use, there are 5 lbs. of the $4 blend and there are 15lbs. of the $2 blend. How many liters of water must be added to 70 L of a 40% acid solution in order to produce a 28% acid solution? Question 2 The Work y=liters of water added to the 30% acid solution

x= liters of water added to the 40% acid solution

.40 + 70 / 70 + x = 28

28 = .28(70 + x)

70 + x = 100

x = 30 liters of water to 40% acid solution

y = 40 liters of water to 28% acid solution Question 3 The Work O=cost of oranges

A=cost of apples

lcm=40 8o+5a=4.09

5o+4a=2.89

40o+25a=20.45

40o+32a=23.12

-7a=-2.67

/-7 /-7

a=$0.40

o=$0.26 Question 4 The Rileys have $27,000 to invest. They intend to invest part of the money in certificates of deposit at 8.5% and the remainder in a savings account at 5%. If they wish to receive the same income from each investment, how much should they invest in each? The Work .085X=.05(27,000-X)

.085X=1,350-.05X

.085X+.05X=1,350

.135X=1,350

X=10,000 INVESTED @ 8.5%

y=17,000 INVESTED @5% x=amount of money invested into the

8.5% account

y=amount of money invested into the 5% acount The perimeter of a rectangle is 52 m. The length is 21/4 times the width. Find the dimensions of the rectangle. Question 5 Question 6 Mr. King is 4 times as old as his daughter. Four years ago, he was 6 times as old as his daughter was then. Find each of their ages. The Work The cost of 24 oranges and 15 apples is $12.36. Fifteen oranges and 12 apples cost $8.67. Find the cost of each orange and each apple. The variables k=Mr.kings age d=the age of his daughter Equations k=4d k= Mr.King's age

d=his daughters age Question 8 w = 120 ft^2

w = 120/l or l = 120/w;

2l + 2(120/l) = 52 ft or 2(120/w) + 2w = 52 ft

2l + 240/l = 52 ft or 240/w + 2w = 52 ft

2l^2 + 240 = 52l or 240 + 2w^2 = 52w

2l^2 - 52l + 240 = 0 or 2w^2 - 52w + 240 = 0

2(l^2 - 26l + 120) = 0 or 2(w^2 - 26l + 120) = 0

2(l-6)(l-20) = 0 or 2(w-6)(w-20) = 0

l = 6 or 20; w = 6 or 20 The Work

k=4d

k-4=6(d-4)

4d-4=6(d-4)

4d-4=6d-24

-4d -4d

-4=2d-24

+24 +24

20=2d

/2 /2

10=d

k=4(10)

k=40

d=10 Since the

equations

aren't lined

up,we use

substitution. 2l + 2w = 52 ft

lw = 120 ft^2 Question 7 In Blue River, Terry can row 36 km downstream in 3 hours but it takes him 6 hours to row that same distance upstream. Find the rate he rows in still water and the rate of the current. QUESTION 10 The sum of the digits of a certain two-digit number is 6. If the original number is subtracted from the number formed by interchanging the digits. The result is 36. Find the original number. 2l + 2w = 52 ft

lw = 120 ft^2 Variables A car started out from a Memphis toward Litter Rock at the rate of 60km/h. A second car left from the same point 2 hours later and drove along the same route at 75km/h. How long did it take the second car to overtake the first car? The work Define the Variables t=digit in the tens place

o=digit in the ones place The Work t+o=6

10o+t-(10t+o)=36

10o+(6-o)-10(6-o)-o=36

10o + 6-o -60+10o -o = 36

18o - 54 = 36

18o = 90

o = 5

t+5=6

t=1

so the answer is 15 60(y+2)-75y=0

60y+120-75x=0

-15y+120=0

-15y+120=0-120(Subtract 120 each side)

-15y=-120

-15y/-15=-120/-15(Divide -15 each side)

y=8 You are 36 miles from a friend. You both start riding your bicycles toward each other at the same time. You travel 15 miles per hour and your friend travels 3 miles per hour slower. How far will you travel before you meet your friend? Question 9 Variables

y=your distance

f=friend's distance The Work

d=r(t)

15t+12t=36

27t=36

t=4/3hrs

15(4/3)+12t=36

20+12t=36

Since 20 miles is your distance

and your friend's is 16 miles. You are riding 15mi/h

and your friend is

riding 12mi/h.

your equation=

15(t)=d

friends equation=

12(t)=d x=speed of boat in water

y=speed of the current The Work 36/3=12km going downstream

36/6=6km going upstream

x+y=12

x-y=6

2x=18

x=9

Now we check.

9+y=12

y=3

So the boat is going 9km/h

and the current is going

3km/hr THE END Those were our ten

problems.We hope you

understood. THANK YOU LOL AND NOW WE HOPE U AREN'T ANNOYED

BY THIS YET. NO:ENJOY! YES:CLICK NEXT

SLIDE And now enjoy

a few songs...=) THANK YOU FOR WATCHING! GOOD BYE... Define the veriables x = the time of the first car y = the time of the second car Because the second car overtaked the first car so we have the first equation:

60x=75y ----> 60x-75y=0 The second car left 2 hours later so we have second equation: x=y+2 60x-75y=0 x=y+2 x=y+2

x=8+2

x=10 So the time of the first car is 10 hours and the second car is 8 hours. We use substitution

because the equations

are not lined up. HI GUYS l=length

w=width

Full transcriptBy:Anthony Lopez

Joseph Nguyen

Bao Le

Eliseo Canela

Vincent Nguyen The Mixture Problems In our presentation, we

will present you 10 question

about mixture problems

that we have covered in class. Question 1: A special tea blend is made from two varieties of herbal tea,

one that cost $4.00/lb and another that cost $2.00/lb. How many pounds of each type are needed to make 20 pounds of a blend worth $2.50/lb? Define the variables:

x= pounds of the $2.00 herbal tea

y= pounds of the $4.00 herbal tea Lets begin doing the problems The Work

x+y=20

2x+4y=20(2.5)

2x+4y=50

2(x+y=20)

2x+4y=50

2x+2y=40

- - -

2x+4y=50

-2y=-10

/-2 /-2

y=5 We choose

elimination

because

the equations

are lined up. And now we subtract Since there are only 20 pounds of use, there are 5 lbs. of the $4 blend and there are 15lbs. of the $2 blend. How many liters of water must be added to 70 L of a 40% acid solution in order to produce a 28% acid solution? Question 2 The Work y=liters of water added to the 30% acid solution

x= liters of water added to the 40% acid solution

.40 + 70 / 70 + x = 28

28 = .28(70 + x)

70 + x = 100

x = 30 liters of water to 40% acid solution

y = 40 liters of water to 28% acid solution Question 3 The Work O=cost of oranges

A=cost of apples

lcm=40 8o+5a=4.09

5o+4a=2.89

40o+25a=20.45

40o+32a=23.12

-7a=-2.67

/-7 /-7

a=$0.40

o=$0.26 Question 4 The Rileys have $27,000 to invest. They intend to invest part of the money in certificates of deposit at 8.5% and the remainder in a savings account at 5%. If they wish to receive the same income from each investment, how much should they invest in each? The Work .085X=.05(27,000-X)

.085X=1,350-.05X

.085X+.05X=1,350

.135X=1,350

X=10,000 INVESTED @ 8.5%

y=17,000 INVESTED @5% x=amount of money invested into the

8.5% account

y=amount of money invested into the 5% acount The perimeter of a rectangle is 52 m. The length is 21/4 times the width. Find the dimensions of the rectangle. Question 5 Question 6 Mr. King is 4 times as old as his daughter. Four years ago, he was 6 times as old as his daughter was then. Find each of their ages. The Work The cost of 24 oranges and 15 apples is $12.36. Fifteen oranges and 12 apples cost $8.67. Find the cost of each orange and each apple. The variables k=Mr.kings age d=the age of his daughter Equations k=4d k= Mr.King's age

d=his daughters age Question 8 w = 120 ft^2

w = 120/l or l = 120/w;

2l + 2(120/l) = 52 ft or 2(120/w) + 2w = 52 ft

2l + 240/l = 52 ft or 240/w + 2w = 52 ft

2l^2 + 240 = 52l or 240 + 2w^2 = 52w

2l^2 - 52l + 240 = 0 or 2w^2 - 52w + 240 = 0

2(l^2 - 26l + 120) = 0 or 2(w^2 - 26l + 120) = 0

2(l-6)(l-20) = 0 or 2(w-6)(w-20) = 0

l = 6 or 20; w = 6 or 20 The Work

k=4d

k-4=6(d-4)

4d-4=6(d-4)

4d-4=6d-24

-4d -4d

-4=2d-24

+24 +24

20=2d

/2 /2

10=d

k=4(10)

k=40

d=10 Since the

equations

aren't lined

up,we use

substitution. 2l + 2w = 52 ft

lw = 120 ft^2 Question 7 In Blue River, Terry can row 36 km downstream in 3 hours but it takes him 6 hours to row that same distance upstream. Find the rate he rows in still water and the rate of the current. QUESTION 10 The sum of the digits of a certain two-digit number is 6. If the original number is subtracted from the number formed by interchanging the digits. The result is 36. Find the original number. 2l + 2w = 52 ft

lw = 120 ft^2 Variables A car started out from a Memphis toward Litter Rock at the rate of 60km/h. A second car left from the same point 2 hours later and drove along the same route at 75km/h. How long did it take the second car to overtake the first car? The work Define the Variables t=digit in the tens place

o=digit in the ones place The Work t+o=6

10o+t-(10t+o)=36

10o+(6-o)-10(6-o)-o=36

10o + 6-o -60+10o -o = 36

18o - 54 = 36

18o = 90

o = 5

t+5=6

t=1

so the answer is 15 60(y+2)-75y=0

60y+120-75x=0

-15y+120=0

-15y+120=0-120(Subtract 120 each side)

-15y=-120

-15y/-15=-120/-15(Divide -15 each side)

y=8 You are 36 miles from a friend. You both start riding your bicycles toward each other at the same time. You travel 15 miles per hour and your friend travels 3 miles per hour slower. How far will you travel before you meet your friend? Question 9 Variables

y=your distance

f=friend's distance The Work

d=r(t)

15t+12t=36

27t=36

t=4/3hrs

15(4/3)+12t=36

20+12t=36

Since 20 miles is your distance

and your friend's is 16 miles. You are riding 15mi/h

and your friend is

riding 12mi/h.

your equation=

15(t)=d

friends equation=

12(t)=d x=speed of boat in water

y=speed of the current The Work 36/3=12km going downstream

36/6=6km going upstream

x+y=12

x-y=6

2x=18

x=9

Now we check.

9+y=12

y=3

So the boat is going 9km/h

and the current is going

3km/hr THE END Those were our ten

problems.We hope you

understood. THANK YOU LOL AND NOW WE HOPE U AREN'T ANNOYED

BY THIS YET. NO:ENJOY! YES:CLICK NEXT

SLIDE And now enjoy

a few songs...=) THANK YOU FOR WATCHING! GOOD BYE... Define the veriables x = the time of the first car y = the time of the second car Because the second car overtaked the first car so we have the first equation:

60x=75y ----> 60x-75y=0 The second car left 2 hours later so we have second equation: x=y+2 60x-75y=0 x=y+2 x=y+2

x=8+2

x=10 So the time of the first car is 10 hours and the second car is 8 hours. We use substitution

because the equations

are not lined up. HI GUYS l=length

w=width