options: Analyze and solve linear equations and pairs of simultaneous linear equations.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Solve systems of equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Use the four operations with whole numbers to solve problems.

Multiply and divide within 100.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Understand the connections between proportional relationships, lines, and linear equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Work with equal groups of objects to gain foundations for multiplication.

Perform arithmetic operations on polynomials.

Understand solving equations as a process of reasoning and explain the reasoning.

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Understand properties of multiplication and the relationship between multiplication and division.

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Gain familiarity with factors and multiples.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
problem_activity: Problem 1
A clothing manufacturer has to use at least 1,000 yards of cotton to make room for new inventory to make shirts and pajamas. A shirt requires 1 yard of fabric, and a pair of pajamas requires 3 yards of fabric. It takes 2 hours to make a shirt and 3 hours to make a pair of pajamas, and there are 1600 hours available to make all of the clothing. Let
$$x$$
represent the number of shirts and
$$y$$
represent the number of pajamas.
What is the smallest number of pajamas the manufacturer can make and meet all of these conditions?
Problem 2
Phil and Cath make and sell boomerangs for a school event. The money they raise will go to charity. They plan to make them in two sizes: small and large.
Phil will carve them from wood.
The small boomerang takes 2 hours to carve, and the large one takes 3 hours to carve.
Phil has a total of 24 hours available for carving.
Cath will decorate them. She only has time to decorate 10 boomerangs of either size.
Phil and Cath want to make as much money for charity as they can.
The small boomerang will make $8 for charity.
The large boomerang will make $10 for charity.
How many small and large boomerangs should they make?
How much money will they then make?


correct_option_index: 22

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