Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.9 Dependent and Independent Variables and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 5 Lesson 5.9 Dependent and Independent Variables Answers Key
Sometimes word problems contain dependent and independent variables. The dependent variable in a problem is the value that is affected by the other values in the problem. The independent variable is the value that affects the outcome of t
he dependent variable.
If a car has to travel 200 miles, the speed (s) the car is driving is the independent variable and the time (f) it takes to make the trip is the dependent variable. This can be represented by the formula, 200 = s × t, and can be solved by creating a table.
Use tables to identify the variables and find possible solutions to the problems.
Question 1.
Maria has to buy apples at the grocery store. Apples cost $ 1.25 per pound. How much will Maria spend on apples?
What equation will you use? __________
Answer:
Given cost of Apples = $1.25 per pound
Let us assume the Over all cost of Apples = y (which is an Dependent variable)
X be the independent variable which is in pounds
Equation: y = 1.25 x 
Question 2.
When a tree is planted, it is 6 feet tall. Each month, it grows by 2 feet. How tall will it get over time?
What equation will you use? _____
Answer:
Height of tree planted = 6 feet
Height of tree grows on Every month = 2 feet
Height of tree get over time = (h) = ?
Equation: h = (6 + x).2
Case(i) : Height of tree in 3 months : h = (6 +x ).2
= (6+3).2
= 9.2
= 18 feet
Case(ii) : Height of tree in 6 months : h = (6 +6 ).2
= (6+6).2
= 12.2
= 24 feet
Case(iii) : Height of tree in 3 months : h = (6 +x ).2
= (6+48).2
= 54.2
= 108 feet
Use tables to identify the variables and find possible solutions to the problems.
Question 1.
Students have been assigned to read a book that is 150 pages. Every student reads at a different speed. Depending on reading speed, how many days will it take different students to read the assigned book?
Write the equation: ________________
Answer:
Number of pages assigned for students to read = 150
Number of days it take at different speed for reading the assigned book = n = ?
Equation: n = 150 / Reading Speed
Number of days at a speed of 15 : n = 150 / 15 = 10 days
Number of days at a speed of 20 : n = 150 / 20 = 7.5 days
Number of days at a speed of 20 : n = 150 / 30 = 5 days
Question 2.
As a candle burns, it decreases in height by 2 inches every hour. If the candle is 12 inches tall when it is lit, how will the height change over time?
Write the equation: ____________
Answer:
Height of candle decreases for every hour = 2
Height of candle = 12
Equation: h = h – 2t
Case(i) : Height of candle in 1 hour : h = h – 2.1
= 12 – 2
= 10
Case(ii) : Height of candle in 2 hour : h = h – 2.2
= 12 – 4
= 8
Case(iii) : Height of candle in 3 hour : h = h – 2.3
= 12 – 6
= 6
Question 3.
As a daffodil grows, it increases in height by 3 inches every 2 days. If the daffodil plant starts at 1 inch, how will the height change over time?
Write the equation: ______________
Answer:
Initial height of daffodil = 1 inch
Increase of height for every 2 days = 3
Equation : initial height + height increases for every 2 days
case(i) : for 2 days = 1+ 2 = 3
case(ii) : for 4 days =1 + 3+3 = 7
case(ii) : for 6 days = 1+3+3+3 = 10
case(ii) : for 8 days = 1+3+3+3+3= 13
Question 4.
The temperature in an oven increases by 8° every minute. If the starting temperature of the oven is 250°, how will the temperature change over time?
Write the equation: _________________
Answer:
Initial temperature of oven = 250°
Temperature increasing every minute = 8°
Temperature changing over time (T) = ?
Equation: T = 250 + 8t
Case(i): When time t = 1 minute
T = 250 + 8.1
= 250 + 8
= 258
Case(ii): When time t = 2 minute
T = 250 + 8.2
= 250 + 16
= 266
Case(iii): When time t = 3 minute
T = 250 + 8.3
= 250 + 24
= 274
Case(iv): When time t = 4 minute
T = 250 + 8.4
= 250 + 32
= 282
