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| 7 Theory slides |
| 9 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Mark has just started working with his father at a car dealership. They sell cars and motorcycles.
Zain volunteered to work at the reception desk at the school concert.
At the end of the evening, they picked up the cash box and noticed a dollar lying on the floor next to it. Zain wonders whether the dollar belongs inside the cash box or not.
Without considering the extra dollar found on the floor, write and solve a system of equations. Does the solution make sense in this context?
(I): LHS−x=RHS−x
(II): y=47−x
(I): LHS−x=RHS−x
(II): y=47−x
(II): Distribute 4
(II): Subtract term
(II): LHS−188=RHS−188
(I): x=13
(I): Subtract term
Write and solve a system of equations.
(I): LHS⋅2.5=RHS⋅2.5
(II): Subtract (I)
Tiffaniqua is selling juice to make some money for a trip to the beach. To prepare a big jug, she used oranges and peaches.
Tiffaniqua's math teacher stopped by to buy some juice and told her the amount of carbohydrates that oranges and peaches have.
Write and solve a system of equations.
(I): LHS−x=RHS−x
(II): LHS−12x=RHS−12x
(II): LHS/8=RHS/8
(II): Write as a sum of fractions
(II): ca⋅b=ca⋅b
(II): Put minus sign in front of fraction
(II): ba=b/4a/4
(II): Calculate quotient
Finally, the point of intersection can be determined.
The lines intersect at the point with coordinates (6,7). Therefore, the solution to the system is x=6 and y=7. In the context of the situation, this means that Tiffaniqua used 6 oranges and 7 peaches to prepare a jug of juice.
Adventures on the Water is a company that organizes river safaris in Sri Lanka. They take tourists on boats along a river in the middle of the jungle for a full day.
Each boat can hold at most 8 people and can only carry 1200 pounds of weight, including passengers and gear, for safety reasons. The company assumes that, on average, an adult weighs 150 pounds and a child weighs 75 pounds. It is also assumed that each group will require 200 pounds of gear plus 10 pounds of gear per person. There are three groups who wish to take a river safari.
Write and solve a system of inequalities.
(I): LHS−x=RHS−x
(II): LHS−200=RHS−200
(II): LHS−160x=RHS−160x
(II): LHS/85=RHS/85
(II): Write as a sum of fractions
(II): Put minus sign in front of fraction
(II): ca⋅b=ca⋅b
(II): ba=b/5a/5
By following the same procedure, the region that corresponds to the second inequality can be determined.
Test Point: (1,2) | ||
---|---|---|
Inequality | Substitute | Simplify |
x+y≤8 | 1+2≤?8 | 3≤8 ✓ |
160x+85y+200≤1200 | 160(1)+85(2)+200≤?1200 | 230≤1200 ✓ |
The second inequality is also satisfied by (1,2). Therefore, the region that contains this point will be shaded.
To fully see the region that satisfies both inequalities, the unwanted regiones will be removed.
Finally, a point that represents each of the three groups will be plotted to see if they belong to the shaded area.
Group | Adults & Children | Point |
---|---|---|
A | 4 adults and 2 children | (4,2) |
B | 3 adults and 5 children | (3,5) |
C | 8 adults | (8,0) |
These points will be plotted on the coordinate plane.
The points that represent groups A and B are in the shaded area, and the point that represents group C is not in the shaded area. Therefore, A and B are the only groups that can safely take a river safari.
The challenge presented at the beginning of the lesson can also be modeled by a system of equations. It is known that Mark and his father sell cars and motorcycles.
Write and solve a system of equations.
(I): LHS−x=RHS−x
(II): y=-x+18
(II): Distribute 2
(II): Subtract term
(II): LHS−36=RHS−36
(II): LHS/2=RHS/2
(I): x=7
(I): Add terms
We know that 675 of the total parking spots are occupied by either cars or motorcycles. If we call the number of cars c and the number of motorcycles m, we can write the following equation. c+m=675 Furthermore, the ratio of cars to motorcycles is 8:1. This means that the number of cars over the number of motorcycles is 81. c/m = 8/1 Let's solve this proportion for c.
Now we have two equations that describe the parking situation on this specific day. This allows us to write a system of equations that we can solve for c and m by using the Substitution Method.
We do not need to find the value of c because we are only interested in the motorcycles. There are 75 motorcycles in the parking place, which means that 100-75=25 motorcycle spots are vacant.
Dylan is buying 100 fish for his new aquarium.
He wants to buy angelfish, cyprinids, and cichlids.
Let's start by defining variables. Let x, y, and z be the number of angelfish, cyprinids, and cichlids, respectively, that Dylan buys. We know that he buys is 61 more angelfish than he does cichlids. Let's express it as an equation. x=z+61 We also know that the total number of fish Dylan buys is 100. In other words, the sum of the variables is equal to 100. x+y+z=100 Finally, we know that he spends a total of $3000. To write the third equation, keep in mind the price of each fish! 10x+50y+200z=3000 With these equations, we can form a system of three equations, which we can then solve by using the Substitution Method.
Next, we will isolate y in Equation (II), substitute the equivalent expression into Equation (III), and solve for z. Let's do it!
Now that we know that z=4, we can substitute this value into Equation (I) and Equation (II). This will allow us to find the values of x and y.
We found that Dylan buys 65 angelfish, 31 cyprinids, and 4 cichlids.