$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

Problem Solving

Multi-Step Equations

Simple and Compound Interest

Multi-Step Inequalities

Transforming Formulas

Problem Solving for $100

Find 4 consecutive even integers whose sum is 228

Let x be the smallest of the numbers. Then, the other numbers will be x+2, x+4 and x+6

x + (x+2) + (x+4) + (x+6) = 2284x + 12 = 2284x = 216x = 54. So the other numbers are 56, 58 and 60

Answer

Back

Problem Solving for $200

An item is on sale for 30% off the original price. The final sale price is $42.65. What was the original price?

Answer

Back

Let x = the original price of the item. Then:x - 0.3x = $42.650.7x = $42.65x = $60.93

Problem Solving for $300

Andy puts a certain amount of money into a bank account. When he withdrew the money from the account he had $558.45. If this is 9.5% more than he started with, how much money did he deposit into the account?

Answer

Back

Let x = the amount of money he started with. Then:

x + 0.095x = $558.45

1.095x = $558.45

x = $510

Problem Solving for $400

If the perimeter of a rectangle is 64cm and the length is 10cm less than twice the width. What is the length and width of the rectangle?

P = 2(L+w)let x = the width. Then:2x – 10 = L so,64 = 2(2x – 10 + x)32 = (2x + x – 10)32 = 3x – 1042 = 3x14 = x so, the width = 14 and the length = 2(14) -10 = 28-10 = 18cm

Answer

Back

Problem Solving for $500

The cost of renting a car is $50 per day plus 15 cents per mile driven. If Amy rented the car for three days and paid a total of $217.50, how many miles did she drive?

Answer

Back

Let x = the # of miles driven. Then,$217.50 = 50(3) + 0.15x217.50 = 150 + .15x67.50 = .15xx = 450 miles

Multi-Step Equations for $100

Solve for x:

3x = x/3

Answer

3x = x/3

9x = x

8x = 0

x = 0Back

Multi-Step Equations for $200

Solve for C:

7 + 2(3 + C) = 2(3 + 7) + C

Answer

7 + 2(3 + C) = 2(3 + 7) + C

7 + 6 + 2C = 6 + 14 + C

13 + 2C = 20 + C

2C = 7 + C

C = 7

Back

Multi-Step Equations for $300

Solve for d:

7.25d + 2d – 5d – 2 = 4d + 3

Answer

7.25d + 2d – 5d – 2 = 4d + 34.25d – 2 = 4d + 30.25d – 2 = 30.25d = 5d = 20

Back

Multi-Step Equations for $400

Solve for n.

(1/3)(n + 9) – 5 = 7

Answer

Back

(1/3)(n + 9) – 5 = 7

(1/3)(n + 9) = 12

n+9 = 36

n = 27

Multi-Step Equations for $500

Solve for p.

4p – 4 = 2(p+3) – 6(9-p)

Answer

Back

4p – 4 = 2(p+3) – 6(9-p) 4p – 4 = 2p + 6 – 54 + 6p 4p – 4 = 2p + 6p + 6 – 54 4p – 4 = 8p – 48 -4 = 4p – 48 44 = 4p p = 11

Multi-Step Inequalities for $100

Solve for x:

x/(3) + 3 > 5

Answer

x/(3) + 3 > 5x/(3) + 3 - 3 > 5 - 3x/(3) > 2x/(3) * 3 > 2 * 3X > 6

Back

Multi-Step Inequalities for $200

Solve for x:

-5x + 20 ≤ 10

Answer

-5x + 20 ≤ 10 -20 -20-5x ≤ -10(-5x)/(-5)≤ (-10)/(-5)X ≥ 2

Back

Multi-Step Inequalities for $300

Replace the with a number that makes the inequalities equivalent

-3x >

x < -9

Answer

-3x > (-3x)/(-3) > / (-3)x < /(-3) and x < -9So, /(-3) = -9 /(-3) * -3 = -9 * -3 = 27

Back

Multi-Step Inequalities for $400

Solve for x:

-(x-6) + 5 - 2x < 8

Answer-(x-6) + 5 - 2x < 8-(x-6) + 5 - 5 - 2x < 8 – 5-(x-6) - 2x < 3-x + 6 – 2x < 3-3x + 6 < 3-3x + 6 – 6 < 3 – 6-3x < -3(-3x)/(-3) < (-3)/(-3)X > 1

Back

Multi-Step Inequalities for $500

Solve for x.

10x – 5 - 3x > 3 – (5 - x)

Answer10x – 5 - 3x > 3 – (5 - x)7x – 5 > 3 – 5 + x7x – 5 > -2 + x7x > 3 + x6x > 3x > 0.5

Back

Check 1: (Substitute it in –> Should be equal)

10(0.5) – 5 – 3(0.5) = 3 – (5 – (0.5))

5 - 5 – 1.5 = 3 - 4.5

-1.5 = -1.5

Check 2: (Pick value that is true)

Let x = 1

10(1) – 5 – 3(1) > 3 – (5 – (1))

10 - 5 – 3 > 3 - 4

2 > -1 => True

Check 3: (Pick value that is false)

Let x = 0

10(0) – 5 – 3(0) = 3 – (5 – (0))

-5 > 3 - 5

-5 > -2 => FALSE

Transforming Formulas for $100

Solve for x:

y = -2x + 5

Answer

y = -2x + 5

y - 5 = -2x

y-5 = x

-2

Back

Transforming Formulas for $200

Solve for m:

n = 4p + 5m

Answern = 4p + 5mn – 4p = 5m

n – 4p = m

5

Back

Transforming Formulas for $300

Solve for p:

2t = s/4 – 8p

Answer

2t = s/4 – 8p

2t – s/4 = -8p

-t + s = p

4 32

Back

Transforming Formulas for $400

Solve for y:

7y – 3x = 2m

4 2

Answer

7y – 3x = 2m

4 2

7y – 6x = 8m7y = 8m + 6x y = 8m + 6x

7Back

Transforming Formulas for $500

Solve for c:

C – 3m + 5 = 2n

2

Answer

C – 3m + 5 = 2n 2C – 3m = 2n - 5 2C – 3m = 2(2n – 5)C – 3m = 4n – 10C = 4n + 3m – 10

Back

Simple and Compound Interest for $100

Write the formula for simple interest.

Answer

I = prt

I: Interest

p: Principal

r: Rate

t: Time

Back

Simple and Compound Interest for $200

Write the formula for compound interest:

Answer

B = p(1+r)n

B: Balancep: Principalr: Raten: Number of times interest is

compounded

Back

Simple and Compound Interest for $300

If Jane put $800 into a bank account which pays 3.25% simple interest annually for 4 years, how much money did she have at the end?

Answer

I = prtI = 800 * 0.0325 * 4I = 104

Total = p +I = 800 + 104 = $904

Back

Simple and Compound Interest for $400

Find the balance if $675 is deposited in an account which pays 3.75% interest compounded annually for 4 years.

AnswerB = p(1+r)n

Compounded Annually:

p = $675

r = 3.75%

n = 4 years

B = 675(1 + .0375)4

B = $782.09

Back

Simple and Compound Interest for $500

Find the balance if $29,200 is deposited in an account which pays 2.4% interest compounded quarterly for 3 years.

Answer

Back

B = p(1+r)n

Compounded Quarterly:

p = $29,200

r = 2.4% = .024/4 (quarterly) = .006

n = 3 years * 4 = 12 times

B = 29,200(1 + .006)12

B = $31,373.19