Apples are 99 cents a pound, and pears are 1.25 a pound. If I spend 4 and the weight of the ap

step 1 Hello, so here we're going to set up a 4 being equal to 1 .98x plus 1 .25x. And that's going to

Apples are 99 cents a pound, and pears are 1.25 a pound. If...

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Key Concepts

System of Linear Equations

This concept involves forming and solving equations that represent multiple conditions from a problem. When a scenario includes relationships such as total cost and weight ratios, each condition can be translated into a separate equation, which collectively form a system that can be solved to find the unknown quantities.

Ratios

Ratios express the relative sizes of two or more quantities. In many word problems, a specified ratio, such as one weight being a multiple of another, provides a relationship that can be incorporated into an equation to help determine the actual amounts involved.

Unit Price Calculations

This involves understanding and applying the cost per unit in problems where items are priced individually. By multiplying the weight or quantity of an item by its cost per unit, one can determine the total expenditure for that item, which is essential in setting up equations based on total cost constraints.

Variable Substitution Method

The substitution method is a technique used to solve systems of equations, where one equation is solved for one variable and then substituted into another equation. This is particularly useful when one variable is defined in terms of another, as it simplifies the system into a single equation that is easier to solve.

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