Chapter 2: Equations in One Variable

Rational Coefficients

100

-1.4 d = 0.7

d= -.5

200

4 1/6 = 3 1/3c

c= 1 1/4

300

-9 5/8w = 108

w= -11 17/77

400

-5.6k = -12.88

k= 2.3

500

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels. Define a variable. Then write and solve an equation to find how may bagels there were in the bakery.

1/3b = 72, 216 bagels

Solve Two Steps

100

3x +2 =20

x=6

200

1 2/3 m + 2 = 2 1/6

m= 1/10

300

-14.2 = -4.2 g + 6.8

g=5

400

(n/-3) - 2= 18

n = 48

500

Some friends decide to go to the aquarium together. Each person pays $7.50 to get in. They spend a total of $40 for the shark exhibit. The total cost is $70. Solve to find how many people went to the aquarium. 

7.5x +40=70, 4 people

Write Two Step

100

Twelve is twenty less than eight times a number.

12= 8x - 20, x=4

200

The difference between a number divided by four and seven is twenty-one.

x/4 -7 =21, x= 112

300

The sum of a number times seven and two is negative nineteen.

7x + 2= -19,  x=-3

400

Beth and some friends went to the movies. They bought 4 drinks and 2 tubs of popcorn and spent a total of $32.50 on the food. Each drink costs $3.50 less than a tub of popcorn.

a. Define a variable. Write an equation that can be used to find the cost of one tub of popcorn

2t + 4 (t - 3.5) =32.5

500

Beth and some friends went to the movies. They bought 4 drinks and 2 tubs of popcorn and spent a total of $32.50 on the food. Each drink costs $3.50 less than a tub of popcorn.

b. Solve the equation to find the cost of a drink.

each drink costs $4.25

Variables on Both Sides

100

-w = -10 + 4w

w=2

200

8a = 5a+21

a=7

300

3x - 7= 8x +23

x= -6

400

An online movie streaming plan charges an annual fee of $45 plus $2.50 per movie watched. Another plan has no annual fee but charges $3.75 per movie watched. For how many movies is the cost of the plans the same?

2.5x + 45 = 3.75x, x=36 movies

500

The table shows the number of points scored by three players in last night’s basketball game. If Bill and Greg scored the same number of points, how many points did Steve score?

Steve: 2x

Greg: 2x+8

Bill: 3x-4

Steve scored 24 points

Multi-Step

100

-50 = -2(a + 3)

a=22

200

4(x - 2) = 2(x - 4) + 2x

{identity}

300

5(y - 2) - 2 = 2(y + 1) - 5

y=3

400

-4(p + 1) = 2(8 - 2p)

{null set}

500

Mr. Richards' class is holding a canned food drive for charity. Juliet collected 10 more cans than Rosana. Santiago collected twice as many cans as Juliet. If they collected 130 cans altogether, how many cans did Juliet collect?

x+(x+10)+2(x+10)=130, 35 cans