standard_description: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^(2 )+ y^(2) = 3.
problem_activity: Problem 1
Act 1: Look at the following recipe -
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What do you notice? What do you wonder?
Problem 2
Act 2: Use the following information to determine how many batches of cake can be made, how many servings can be made, and how much of each ingredient are needed to make that much cake -
This is how many eggs there are:
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This is how much oil there is:
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There are 4 boxes of cake mix.
Water will come from the tap.
Each box of cake makes 12 servings.
Problem 3
Act 3: Reveal the answer –
There is enough of each ingredient to make
$$2\frac{2}{3}$$
boxes, which would produce 32 servings of cake.
To make
$$2\frac23$$
boxes, you need
$$2\frac23$$
cups of water,
$$\frac89$$
cups of vegetable oil, and 8 eggs.
Was your answer reasonable? Why or why not?
Problem 4
Act 4 (the sequel):
Keaton wants to make enough cake so that every student in his fifth grade could have some. There are 100 students in fifth grade. How much more of each ingredient above would Keaton need?


aligns: no