Solved Examples and Worksheet for Describing Change in One Variable Affecting the Other

Q1Brian rolls a four-sided die (numbered 1 to 4) and a ten-sided die numbered 1 to 10). What is the probability that the outcome of the 1st die is a number greater than 1 and the outcome of the 2nd die is a number less than 7?

A. 1120
B. 720
C. 920
D. None of the above

Solutions
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Step: 1
The two events are independent events.
Step: 2
Numbers greater than 1 on 1st die are 2, 3 and 4, which are 3 in number.
Step: 3
Numbers less than 7 on 2nd die are 1, 2, 3, 4, 5 and 6, which are 6 in number.
Step: 4
P(number > 1 on 1st die = Number of favorable outcomes / Total number of possible outcomes = 34
Step: 5
P(number < 7 on 2nd die = Number of favorable outcomes / Total number of possible outcomes = 610
Step: 6
P(number > 1 on 1st die number < 7 on 2nd dice) = P (number > 1 on 1st dice) x P (number < 7 on 2nd dice)
Step: 7
= 34 x 610 = 920
  [Substitute and multiply.]
Step: 8
Probability that the outcome of the 1st die is a number greater than 1 and the outcome of the 2nd die s a number less than 7 is 920.
Correct Answer is :   920
Q2Which one represents 24,527 in words?
A. two thousand forty five hundred twenty seven
B. twenty thousand forty five hundred twenty seven
C. twenty four thousand five hundred twenty seven
D. twenty four hundred fifty seven

Solutions
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Step: 1
The word name for the number 24,527 is twenty four thousand five hundred twenty seven.
Correct Answer is :   twenty four thousand five hundred twenty seven
Q3A plant grows at the rate of 2 inches per month. By how much will it grow in a year?
A. 24 inches
B. 12 inches
C. 2 inches
D. 36 inches

Solutions
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Step: 1
A plant grows at the rate of 2 inches per month.
  [Given.]
Step: 2
Number of months in a year = 12
Step: 3
Number of inches the plant will grow in a year = 2 × 12 = 24
Correct Answer is :   24 inches
Q4Hair of a boy grows 3 cm every month. After how many months will the hair be 60 cm long?
A. 15 months
B. 30 months
C. 25 months
D. 20 months

Solutions
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Step: 1
The hair grows 60 cm in 60 ÷ 3 = 20 months.
Correct Answer is :   20 months
Q5How many weeks will it take for the grass to grow by 1 ft , if it grows at the rate of 2 inches per week?
A. 7 weeks
B. 6 weeks
C. 5 week
D. 8 weeks

Solutions
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Step: 1
Growth of grass in 1 week = 2 inches
Step: 2
Time taken for the grass to grow by 1 feet = 12 × 12 = 6 weeks.
Correct Answer is :   6 weeks
Q6Given that y = 2x + 10 .What will happen to the value of y if the value of x increases by 9?
A. y will be doubled
B. y will increase by 18
C. y remains the same
D. y will increase by 17

Solutions
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Step: 1
y = 2 x + 10
  
Step: 2
y = 2(x + 9) + 10
  [x is increased by 9.]
Step: 3
= 2x + 18 + 10
  
Step: 4
= (2x + 10) + 18 = y + 18
  
Step: 5
So, when x increases by 9, the value of y increases by 18.
Correct Answer is :   y will increase by 18
Q7Given that y = 15x. What will happen to the value of y if x is doubled?

A. the value of y will increase by 12
B. the value of y remains the same
C. the value of y is doubled
D. the value of y will become 2

Solutions
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Step: 1
y = 15x
  
Step: 2
y = 15(2x)
  [x becomes doubled times the original value.]
Step: 3
y = 2x = doubled times the original value.
  
Step: 4
So, when x is doubled, y is also doubled.
Correct Answer is :   the value of y is doubled
Q8Carlos and Maria are on their way to school. Describe how the graph looks like if Carlos is walking at a steady rate faster than Maria.

A. Graph of Carlos walk will be steeper
B. Graph of Maria walk will be steeper
C. Graph of Carlos walk will be greater
D. Graph of Maria walk will be greater

Solutions
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Step: 1
The rate of change of speed for Carlos is greater than the rate of change of speed of Maria.
Step: 2
It is known that the graph with greater rate of change will be steeper.
Step: 3
So, the graph of Carlos walk will be steeper.
Correct Answer is :   Graph of Carlos walk will be steeper
Q9Which of the following statements best suits for the table?
Number of days1234
Rent for CDs$2.00$2.75$3.50$4.25


A. Rental for CD for every additional day increases by $0.75.
B. Rental for CD for every additional day decrease by $0.75.
C. Rental for every additional CD increases by $0.75.
D. Rental for CD for every additional day increases by $2.

Solutions
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Step: 1
The table indicates an amount of $0.75 increase for every additional day.
Step: 2
So, the table best suits the statement 'Rental for CD for every additional day increases by $0.75'.
Correct Answer is :   Rental for CD for every additional day increases by $0.75.
Q10Given that y = 6x. Then, what will happen to the value of y if x is doubled?
A. y will decrease by 2
B. y will increase by 2
C. y will be doubled
D. y will be multiplied by 4

Solutions
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Step: 1
y = 6x
  
Step: 2
y = 6(2x)
  [x is doubled.]
Step: 3
= 12x
= double the original value of y
Step: 4
So, when x is doubled, y is also doubled.
Correct Answer is :   y will be doubled
Q11Given that y = 101x. Then, what will happen to the value of y if x is doubled?
A. y will be doubled
B. y will increase by 2
C. y will increase by 3
D. y will decrease by 2

Solutions
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Step: 1
y = 101x
  
Step: 2
y = 101(2x)
  [x is doubled.]
Step: 3
= 202x
= double the original value of y
Step: 4
When x is doubled, y is also doubled.
Correct Answer is :   y will be doubled
Q12Given that y = 15x. Then, what will happen to the value of y if x is tripled?

A. the value of y is tripled
B. the value of y will become 13 times the original value
C. the value of y will increase by 13
D. the value of y remains the same

Solutions
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Step: 1
y = 15x
  
Step: 2
y = 15(3x)
  [x becomes 3 times the original value.]
Step: 3
y = 45x = 3 times the original value.
  
Step: 4
So, when x is tripled, y is also tripled.
Correct Answer is :   the value of y is tripled

HighSchool Math