Variable Substitution
4x - 5
x = 4
4*4 - 5 = 11
This equation shows how the cost (c) of renting a moving van depends on how many hours (h) it is rented for.
7h = c
What is the independent variable in this scenario?
hours (h)
This equation shows how the length of Pam's essay (p) depends on the number of hours (h) she spends writing this week. How many pages in length is Pam's essay in 5 hours?
p = h + 11
16 pages
6 + a = 13
a = 7
the sum of m and n
m+n
2a + 5
a = 3
2 * 3 + 5 = 11
This equation shows how the total number of pages (p) Alana has read depends on the number of hours (h) she spends reading this week.
p = 17h
What is the dependent variable in this scenario?
total pages (p)
This equation shows how the cost (c) of a cab ride depends on the distance (d) in miles. If a cab ride is 4 miles long, how much will it cost?
c = 2d
$8
a - 14 = 14
a = 28
4 less than a number is 8
a-4=8
3(2y - 1)+6
y = 2
3(2 (2) - 1) + 6 = 15
This equation shows how the number of plants (p) Tiana can have in her backyard is related to the number of seed packets (s) she purchases.
p = s + 12
What is the independent variable in this scenario?
seed packets (s)
Emma got a new 3D printer that can print objects in real life! She wants to print several copies of a toy dinosaur. It takes 4 hours for every dinosaur she wants to print. Write an equation to show the rule for this function. Use (d) for dinosaur and (h) for total hours.
h=4d or 4d=h
a/23 = 5
a=115
multiply k by 5, then subtract 8
5k - 8
3(6-b)+7-2b
b = 4
3(6 - 4) + 7 - 2(4) = 5
Brandon is a member of the football team at his high school. The night before a game, the players enjoy a team dinner provided by their parents. Brandon's mom is making marshmallow treats for dessert. The number of players on the team determines how many treats she will make.
What is the dependent variable in this scenario?
Number of treats
On busy mornings, Rob heats up a toaster pastry for breakfast, but was running low so decided to stock up for later. He has 2 pasteries, but adds 4 for each box he buys. Write and equation to show the rule for total pasteries (p), which depends on the amount of boxes (b) he buys.
2 + 4b = p
Find the value of "a" for each. Which is the greater value?
9a = 27 a/4 = 2
a = 3
5 added to z to the 6th power is a number
z6+5 = b
n/4+2n-3
n = 8
8/4 + 2(8) - 3 = 15
A small apple orchard hires fruit pickers to harvest their crop. The number of apples harvested each day depends on the number of fruit pickers hired.
What is the independent variable?
Number of fruit pickers.
Jen makes checkers gameboards by hand. Each gameboard has 24 games peices.
Create an input/output table to represent how many peices Jen will have made for up to 4 gameboards.
1:24, 2:48, 3:72, 4:96
Travis opened a bag of potting soil that contained an amount of cups of soil. He spilt it evenly among 3 pots. He put a total of 12 cups of soil in the pots. Create an equation to represent the problem and solve.
x/3=12 36 cups of soil in the bag
the quotient of a number and 2, plus a number times the value of 6 plus 4
a/2 + b(6+4)