CH 2.3 Shadows and ProportionsProportions and Indirect Measurement

CorrespondingSidesRate

SimilarUnit rate

EXAMPLE #1

A D E

F

B C

AC = 4cmCB = 3CMDF = 12 CMFE = ?

AC = CBDF FE

4 = 312 X

4x = 36 X = 9 FE = 9 CM

?’s 2 - 7

2) 5 / 4 = 20 / FD ; 80/5 = FD ; 16 = FD ; DF = 16cm3) 11/6 = x / 4; 6x = 44; 44/6 = x; x = 7.3333 in4) 15/3 = h /5 ; 15*5 = 3h; h = 25 in5) 7/25 = BC/300; BC = 84 m6) 56/148 = 84/x ; x = 222 mm7) MO = 26ft; 18/24 = 26/x; 34+2/3 ft = MR

?’s 2 - 7

2) 5 / 4 = 20 / FD ; 80/5 = FD ; 16 = FD ; DF = 16cm3) 11/6 = x / 4; 6x = 44; 44/6 = x; x = 7.3333 in4) 15/3 = h /5 ; 15*5 = 3h; h = 25 in5) 7/25 = BC/300; BC = 84 m6) 56/148 = 84/x ; x = 222 mm7) MO = 26ft; 18/24 = 26/x; 34+2/3 ft = MR

8) A car was driven 243.4 miles and used 12 gallons of gas. How many miles could

the car be driven per gallon of gas?

243.4 miles = x miles12 gallons 1 mile

243.4 = 12x X = 20.283

For every gallon of gas, the car could be driven approx 20.3 miles.

?’s 9 – 10

9) 16/11.99 = 1/xX = .75Each roll costs 75 cents, or $0.75

10) 268/14 = x / 1X = 19.1428Everyday Stephanie must read over 20 pages each day to finish on time.

?’s 9 – 10

9) 16/11.99 = 1/xX = .75Each roll costs 75 cents, or $0.75

10) 268/14 = x / 1X = 19.1428Everyday Stephanie must read over 20 pages each day to finish on time.

2.6 Tipping in a Restaurant

Writing a % as a decimal.If your number is larger than 10 percent.##/100 = .##The percent is always out of 100%

% as a decimal100% = 11% = 10%= 9.9%= 1.1%=1%= .1%=

2.6 Tipping in a Restaurant

% as a decimal100% = 1.00 11% = .11

10%= .1 9.9%= .099

1.1%= .0111%= .01

.1%= .001

Fraction to decimal decimal to %

EX ) 5/8 = .625 = .625 * 100 = 62.5%

Tip at a Restaurant

• 10 % bad service• 15 % decent service• ~18% what I like to give• 20 % good service

What percent tip was left for the wait staff?

• Bill was $52.50; tip was $5.5

• Tip / Bill = %/100• 5.5 / 52.5 = % / 100• 5.5 * 100 = 52.5x• 550 = 52.5x • X = 10.476• The tip was only ~10.5 % which means you were

most likely bad service.

What percent tip was left for the wait staff?

• Bill was $52.50; tip was $5.5

• Tip / Bill = %/100• 5.5 / 52.5 = % / 100• 5.5 * 100 = 52.5x• 550 = 52.5x • X = 10.476• The tip was only ~10.5 % which means you were

most likely bad service.

What percent tip was left for the wait staff?

• Bill was $52.50; tip was $5.5

• Tip / Bill = %/100• 5.5 / 52.5 = % / 100• 5.5 * 100 = 52.5x• 550 = 52.5x • X = 10.476• The tip was only ~10.5 % which means you were

most likely bad service.

Bill was $136.24 and the tip was $25.40, how well was your service?

Bill was $136.24 and the tip was $25.40, how well was your service?

• 25.4 / 136.24 = tip %/100

Bill was $136.24 and the tip was $25.40, how well was your service?

• 25.4 / 136.24 = tip %/100

• Tip % = 18.65

• Your service was average because the people left you an 18.65% tip.

You want to leave a certain % tip!

• You usually know the cost of your bill…

• Now instead of the normal equation use

• x/ BILL = tip % / 100

EX) At the hair salon your cut, dye, shampoo, nails, and style cost $135. You want to leave a 16% tip.

• How much is your total bill?

EX) At the hair salon your cut, dye, shampoo, nails, and style cost $135. You want to leave a 16% tip.

• How much is your total bill?

• X = 16• 135 100X = 21.6

EX) At the hair salon your cut, dye, shampoo, nails, and style cost $135. You want to leave a 16% tip.

• How much is your total bill?

• X = 16• 135 100X = 21.6• Your total bill will be $156.60 including the

$21.6 tip.

2.7 Taxes Deducted from Your PaycheckPercents and Taxes

• Tax rate• Gross pay• Net pay• tax

1) The (blank) is a percent used to calculate the amount of money taken out of your gross pay.

2) (Blank) is the total amount of money an employee earns before any taxes or deductions are subtracted.

3) (Blank) is the amount of money that an employee earns after deductions are subtracted from the employee’s gross pay.

4) A (Blank) is a fee that is imposed by the government to pay for public works and services.

Equation is set up very similar to Tip

• When you know the gross pay, taxes, unknown is the %.

• Taxes = % taxes• Gross 100

Working all of my jobs this year I made: Gross pay = $56,000 and I payed Taxes = $13,440.

How much of my income was taxed?

Working all of my jobs this year I made: Gross pay = $56,000 and I payed Taxes = $13,440.

How much of my income was taxed?

13440 = tax rate56000 100

Tax rate = 24%My income was taxed at a rate of 24%.

You grossed $36,000 the year after you graduated college. With a tax rate of 15.6%

how much money do you have to pay the government?

How much of your income is left to live off of?

You grossed $36,000 the year after you graduated college. With a tax rate of 15.6%

how much money do you have to pay the government?

• Taxes paid = 15.6• 36000 100

• You have to pay 5,616 in taxes.

You grossed $36,000 the year after you graduated college. With a tax rate of 15.6%

how much money do you have to pay the government?

• Taxes paid = 15.6• 36000 100

• You have to pay $5,616 in taxes.

• You only have $30,384 left to spend.