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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.
Mark counted 18 vehicles and 50 tires on the lot. Without considering spare tires, use this information to find the number of 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.
The price of tickets for the concert was one ticket for $5 for individuals, or two tickets for $8 for couples. Zain looked inside the cash box and found $200 and ticket stubs for the 47 people in attendance. Does the dollar belong inside the cash box?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.
Then, the teacher asked Tiffaniqua how many oranges and peaches were used in the jug of juice. Tiffaniqua decided to quiz her teacher by telling her that she used a total of 13 fruits and that the jug contains 128 grams of carbohydrates. How many oranges and peaches did she use?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.
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.
In the agency, Mark counted 18 vehicles and 50 tires. Without considering spare tires, use this information to find the number of 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