Solving Equations
If Leah's height is multiplied by 4, it will be 20 cm less than Emma's height. Emma is 210 cm tall. How tall might Leah be?
4L = 210 -20
4L = 190
L = 190/4
L = 47.5cm
Mr. Jung's mass is 45 kg. The mass of his suitcase should be no more than 2.5 times his mass. Write an inequality to model the mass of Mr. Jung's suitcase.
m is less than or equal to 112.5kg
Leo measures the heights of stacks of one, two and three baskets to be 17cm, 19cm and 21 cm. Describe the pattern and develop a formula for the height of the baskets.
h = 17 + 2 (n-1) or h = 2b + 15
What is Canada's current population
40 million
If Mia's height is increased by 50% and then reduced by 10 cm, the result will be 110 cm. What is Mia's original height?
Let M represent Mia's original height
M + 0.5M - 10 = 110
1.5M - 10 = 110
1.5M = 120
M = 120/1.5
M = 80cm
15 is less than or equal to 3x. Give the whole solution set
x= 5,6,7,8,9,10...
Evan measures the height of his bubble tea cups with different amounts of tapioca pearls. He finds the following:
A cup with 1 scoop of tapioca pearls is 11 cm tall.
A cup with 2 scoops of tapioca pearls is 14 cm tall.
A cup with 3 scoops of tapioca pearls is 17 cm tall.
Describe the pattern and develop a formula for the height of a cup with ppp scoops of tapioca pearls.
h = 11 + 3 (p-1) or h = 3p + 8
What is the name of the sport I would like the students to try if the equipment arrives in time?
Tchoukball
A rectangular swimming pool has a length that is 6 meters more than twice its width. The perimeter of the pool is 72 meters. What are the length and width of the pool?
L = 2W + 6
Perimeter = 2L + 2W
2L + 2W = 72
2W+6 + 2W+6 + 2W = 72
6W + 12 = 72
6W = 60
W = 10m
L = 2W + 6
= 2 (10) + 6
= 20 + 6
= 26m
The total cost to renovate a building is less than three times the cost to build a new one. The cost to build a new building is $500,000. Write an inequality to model this situation, and then determine the maximum cost to renovate the building.
Less than $1,500,000.
Who owns the Tim Hortons company?
Burger King
The fence around a triangular garden is in the shape of an equilateral triangle. The side length of the current fence is increased by x cm, and the perimeter of the new fence becomes 5 times the original perimeter. If the perimeter of the original fence is 84 cm, determine the value of x and the new side length of the fence.
Let S be the side length of the original fence
Let X be the increase in the side length of the new fence,
1) Find side length of original triangle as you are given the perimeter.
3s = 84
s = 28cm
2) Find perimeter of bigger triangle
New perimeter = 5 x 84 = 420cm
3) We know that new length is = 28 + x
Use new perimeter and new length to create an algebraic equation
3(28+x) = 420
28 + x = 140
x = 112cm
4) The new side length is 28 + x
= 28 + 112
= 140cm
The total cost to renovate a building is less than four times the cost to build a new one plus $200,000. The cost to build a new building is $620,000. Write an inequality to model this situation, then determine the maximum possible cost to renovate the building.
The maximum cost to renovate the building is less than $2,680,000.
Due to the expansion of the iron in the heat, the Eiffel Tower can increase in height by up to ________ inches during hot summer days.
6