$100 $100 $100 $100 $100

$200

$300

$400

$500

$200 $200 $200 $200

$300 $300 $300 $300

$400 $400 $400 $400

$500 $500$500 $500

Ratios and Unit Rates

Percent of Change

Problem Solving

Proportions Probability

Ratios and Unit Rates for $100

Write a ratio to represent the number of students who got A’s to the number of students who did not:

6 students out of 16 total students got A’s on the Math Test

Answer

Ratio: (Favorable:unfavorable)

6:10 = 3:5

Back

Ratios and Unit Rates for $200

342 m/min = how many m/day?

Answer

342 m/min * 60 min/hr * 24hr/day = 492,480 m/min

Back

Ratios and Unit Rates for $300

A horse is running 10m/s. How many km/hr is he running?

Answer

10m/s * 60s/1min * 60min/1hr * 1km/1000m

= 36,000km/1000hr = 36km/hr

Back

Ratios and Unit Rates for $400

What is the difference between probability and odds?

Answer

Probability = (favorable)/(total)

Odds = (favorable)/(unfavorable)

Back

Ratios and Unit Rates for $500The ratio of boys to girls in a classroom is 3:4. If there are 12

girls in the classroom, how many total students are in the classroom?

Answer

3/4 = x/12

4x = 36

x = 9 boys

So, 9 boys + 12 girls = 21 total students

Back

Percent of Change for $100

What is the percent change on a pair of shoes that originally cost $45, but are on sale for $36?

Answer

(Original – New) / Original * 100

($45 - $36)/ $45 * 100

=($9)/$45 * 100

=.20 * 100

= 20% decrease

Back

Percent of Change for $200

After buying a car for $12,500 a dealer sells the car for $15,750. What is the percent change in the price of the car?

Answer

(Original – New) / Original * 100

(12,500 – 15,750)/ 12,500 *100

= (-3250)/12500 * 100

= -0.26 * 100

= -26%

= 26% Increase

Back

Percent of Change for $300

What is the markup on an ipod if the store buys it for $130 and then increases the price by 53.1%?

Answer

Markup: 130 * 0.531= $69.03

Back

Percent of Change for $400

A store buys a pair of shoes for $12 and then marks them up by 427%. What is the final selling price?

Answer

Back

Markup: 12*4.27 = $51.24

Selling price = $12 + $51.24 = $63.24

Percent of Change for $500

A store decides to have a sale and discounts everything in the store by 35%. If an item originally costs $273, what is the amount of discount and the final selling price?

Answer

Back

Discount: $273 * 0.35 = $95.55

Selling Price = $273 - $95.55 = $177.45

Proportions for $100

Solve for x:

5 = x_

8 20

Answer

5/8 = x/20

8x = 100

x = 12.5

Back

Proportions for $200

Solve for x:

(X-7) = _6_

5 15

Answer

(X-7)/5 = 6/15

5*6 = 15(x-7)

30 = 15x – 105

135 = 15x

9 = x

Back

Proportions for $300

Solve for x:

5 = 12_ (x-3) (x+3)

Answer

5/(x-3) = 12/(x+3)5(x+3) = 12(x-3)

5x + 15 = 12x – 36

15 = 7x – 36

51 = 7x

7.29 = x

Back

Proportions for $400

Given that the triangles below are similar, solve for x and y

10m

14mY

6m

10m X

Answer

Set up two proportions:1) 6m/10m = X/14 10x = 84

x = 8.4m2) 6m/10m = 10/y 100 = 6y 16.67 = y

Back

Proportions for $500

Find the height of the tree given that the boy is 4 feet tall

2.5 ft 10 ft

Answer

Set up a proportion:

2.5ft/10ft = 4/x

Cross Multiply

40 =2.5x

X = 16 ft tall

Back

Probability for $100

If I roll a dice one time, what is the probability of rolling a one or a three?

i.e. P(1 or 3) = ?

Answer

Number of Items in Sample Space = 6

Sample Space {1 2 3 4 5 6}

Probability = 2/6 or 1/3

Back

Probability for $200

If I flip a coin 4 times, what is the probability of the same face showing up all 4 times?

i.e. Either H-H-H-H or T-T-T-T

Answer

Elements in Sample Space = 2*2*2*2 = 16

P(H-H-H-H) = 1/16

P(T-T-T-T) = 1/16

P(H-H-H-H OR T-T-T-T)

= (1/16) + (1/16) = 2/16= 1/8

Back

Probability for $300

Suppose you choose an m&m from a bag containing 5 blue m&m’s, 4 red m&m’s and 7 yellow m&m’s, and the one you pick is blue. You then pick another m&m. Find P(yellow)

Answer

P(yellow)

Number of m&m’s = 5+4+7 = 16

After you pick one blue one there are 15 m&ms left: 4 blues, 4 reds, and 7 yellows. So,

P(yellow) = 7/15

Back

Probability for $400

Draw the sample space (list all possible outcomes) for the following event:

You flip a coin, and then spin the spinner shown below.

Answer

Back

H-O

H-P

H-Y

H-G

H-R

T-O

T-P

T-Y

T-G

T-R{ }

Probability for $500

I spin the spinner shown below, and then roll a dice. Find P(Red and 2)

Answer

Number of elements in sample space:5 * 6 = 30

P(Red) = 1/5P(2) = 1/6

P(Red and 2) = (1/5) * (1/6) = 1/30(There is only one possible outcome out of

the 30 that satisfies the conditions of the event)

Back

Problem Solving for $100

Find three consecutive integers whose sum is 99

Answer

Let x = the smallest of the three integers, then:

x + (x+1) + (x+2) = 993x + 3 = 993x = 96x = 32, x+1 = 33, x+2 = 34

Back

Problem Solving for $200

Find four consecutive EVEN integers whose sum is 108.

AnswerLet x = the smallest of the

four integers, then:x + (x+2) + (x+4) + (x+6) = 1084x + 12 = 1084x = 96x = 24, x+2 = 26, x+4 = 28,

x+6=30

Back

Problem Solving for $300

If Thuy puts $500 into a bank account which pays 3.5% interest every month, how much money will she have after 6 months?

Answer

Back

Time (Months)

Starting Amount

Rate Amount of Increase

Final Amount

1 $500 0.035 $17.50 $517.50

2 $517.50 0.035 $18.11 $535.61

3 $535.61 0.035 $18.75 $554.36

4 $554.36 0.035 $19.40 $573.76

5 $573.76 0.035 $20.08 $593.84

6 $593.84 0.035 $20.78 $614.62

Problem Solving for $400

Andrew has 5 shirts, 3 pants, and 2 pairs of shoes. How many different combinations of outfits of 1 shirt, 1 pair of pants and 1 pair of shoes are possible?

Answer

Ways to solve:

*Make a table of all possible combinations

*Do 5*3*2 = 30 possible combinations.

Back

Problem Solving for $500

The population of HCMC was approximately 6,117,251 in 2004. The annual growth rate is approximately 3%. Assuming these figures are correct, what will the population of HCMC be at the end of 2011?

Answer

Back

Time (year)

Starting Amount

Rate Amount of Increase

Final Amount

2004 6117251 0.03 183517.5 6300768.5

2005 6300768.5 0.03 189023.1 6489791.6

2006 6489791.6 0.03 194693.7 6684485.3

2007 6684485.3 0.03 200534.6 6885019.9

2008 6885019.9 0.03 206550.6 7091570.5

2009 7091570.5 0.03 212.747.1 7304317.6

2010 7304317.6 0.03 219129.5 7523447.1

2011 7523447.1 0.03 225703.4 7,749,151