EQUATIONS AND INEQUALITIES STUDY GUIDE

Determine whether b = 28 is a solution

to b + 78 = 106

QUESTION #1

28 + 78 = 106

ANSWER #1

Solve the equation

s + 3 = 94

QUESTION #2

S = 91

ANSWER #2

The recipe you are using indicates that a mixture should be heated to a temperature of

176 F. The mixture is currently at 94 F. How many more

degrees d does the mixture need to be heated?

QUESTION #3

94 + d = 176

d = 82

ANSWER #3

Solve the equation p – 9 = 57

QUESTION #4

P – 9 = 57

P = 66

ANSWER #4

Write “9 is 12 subtracted from z” as an algebraic equation.

QUESTION #5

9 = z – 12

Z = 21

ANSWER #5

Solve the equation17s = 85

QUESTION #6

17s = 85

S = 5

ANSWER #6

A display has a total of 1900 lights. Each light strand has 50 lights. How many

strands of lights are there?

QUESTION #7

50n = 1900

N = 38

ANSWER # 7

Solve the equation. Check your answer.

M = 10 9

QUESTION #8

M = 90

ANSWER #8

The sugar maple tree in Joshua’s yard is ¼ the age of the oak tree in his yard. The sugar maple tree is 8 years old. How old is the

oak tree?

QUESTION # 9

Sugar Maple = ¼ age of OakSM = ¼ A8 = ¼ A

8 ÷ ¼ = A8 * 4 = A

A = 32

ANSWER #9

A 69-story tower has a height of 828 feet. Write an expression to find the

height of each story. Then, use the expression to find the height of each story.

QUESTION #10

69H = 828H = 828 ÷ 69

H = 12

ANSWER #10

Solve the equationT – 6.6 = 6.88

QUESTION #15

T = 13.48

ANSWER #15

Solve the equation4/5b = 8

QUESTION#16

4/5b = 8B = 8/1 * 5/4

B =10

ANSWER #16

Solve the equation.3j = 1/5

QUESTION # 17

3j = 1/5J = 1/5 * 1/3

J = 1/15

ANSWER # 17

In a fish tank, 6/13 of the fish have a red stripe on them. If 12 of the fish

have red stripes, how many total fish are in the tank?

QUESTION #18

Fish × 6/13 = red stripesF × 6/13 = 12 F = 12 ÷ 6/13 F = 12 × 13/6

F = 26

ANSWER # 18

Luis wants to display leaf specimens for a science fair.

Luis has 76 leaves, which is 45 fewer than the total needed.

Will the science display have a total of 122 leaves, 121 leaves,

31 leaves, or 131 leaves?

QUESTION #19

S – 45 = 76

S = 121 leaves

ANSWER # 19

Hector and Selma play baseball. Selma has 13

trophies. Hector has 5 fewer trophies than Selma has. Write an equation showing this, using

h as the number of trophies Hector has.

QUESTION #20

H = 13 – 5

ANSWER #20

Solve the equation n -14 = 56

QUESTION #21

N – 14 = 56

N = 70

ANSWER #21

Solve the equation5p = 20

QUESTION # 23

5p = 20

P = 4

ANSWER #23

Write an inequality for the situation.

No more than 33 pencils are on the

bench

QUESTION #24

X ≤ 33

ANSWER #24

Wednesday’s low temperature in Indianapolis was 37 F. The same day

in St. Louis, the low temperature was below 74 F, at most how many

degrees warmer was the low temperature in St. Louis, the low temperature in St. Louis than the low temperature in Indianapolis?

QUESTION # 27

At most 37 F

ANSWER #27

Darlene spent $15.25 on supplies to make

lemonade. At least how many glasses of

lemonade must she sell at $0.60 per glass to

make a profit?

QUESTION #29

At least 26 glasses

ANSWER # 29