Solving Multi-Step Equations

Shopping

100

What is the cost of a hoodie priced at $32 after a discount of $5 and an applied tax of 10%? Round to the nearest cent.

$29.50

200

What is the cost of sneakers priced at $100 after a discount of 10% and an applied tax of 10%? Round to the nearest cent.

$99

300

What is the cost of a video priced at $65 after a discount of $12 and an applied tax of 8.5%? Round to the nearest cent.

$57.51

400

What is the cost of a shirt priced at $99 after a discount of 15% and an applied tax of 6.25%? Round to the nearest cent.

$89.41

500

What is the cost of a hoodie priced at $32 and a cap priced at $27, both discounted at 25%? The applied tax is 7.25%. Round the total cost to the nearest cent.

$79.10

Solving by using the distributive property

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

-2(x - 9) = -24

x = 21

500

-13(4 + 2a) = 208

a = -10

How many solutions?

100

2(3n +9) = 30

One solution. n = -8

200

-8x+ 16=-16x + 32

All real numbers (infinitely many)

300

-1/3x+6=3x-6

One solution. 

x=3.6

400

6(-x+4)-1=-6x-9

No solution. 

23=-9

500

6+32x+4 =-32x+40

One solution. 

x=5/16

Equation Grab Bag

100

4x + 9 = 33

x = 6

200

x + 3x = -8

x = -2

300

4(y - 2) + y = -13

y = -1

400

-6(m + 1) + 18 = 24

m = -2

500

7k - 8 + 2(k + 12) = 52

k = 4

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?

n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87

500

When you count by ones fron many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.