Solve each problem. See Example 2. (IMAGE CANNOT COPY)...

Solve each problem. See Example 2. (IMAGE CANNOT COPY) Andrew McGinnis works at Arby's. During one particular day he sold 15 Junior Roast Beef sandwiches and 10 Big Montana sandwiches, totaling $\mathrm{S} 75.25$ Another day he sold 30 Junior Roast Beef sandwiches and 5 Big Montana sandwiches, totaling $\$ 84.65 .$ How much did each type of sandwich cost?

Solve each problem. See Example 2.
(IMAGE CANNOT COPY)
Andrew McGinnis works at Arby's. During one particular day he sold 15 Junior Roast Beef sandwiches and 10 Big Montana sandwiches, totaling $\mathrm{S} 75.25$ Another day he sold 30 Junior Roast Beef sandwiches and 5 Big Montana sandwiches, totaling $\$ 84.65 .$ How much did each type of sandwich cost?

Key Concepts

System of Linear Equations

Systems of linear equations involve two or more equations with multiple unknowns where each equation represents a linear relationship. The solution to the system is the set of values for the unknowns that satisfy all equations simultaneously and is essential in modeling scenarios with multiple constraints.

Variable Representation

This concept involves using symbols to denote unknown quantities, allowing abstract representation and manipulation of the problem's numerical relationships. It forms the foundation for setting up and solving algebraic equations based on the given situation.

Translating Word Problems into Equations

This key concept is about interpreting real-world scenarios and converting the narrative and numerical data into mathematical expressions. It requires identifying the unknown quantities, setting up relationships between them, and forming a system of equations that represents the problem.

Methods for Solving Systems of Equations

There are several strategies to solve systems of equations, such as substitution and elimination. The substitution method involves solving one equation for one variable and then replacing that variable in the other equation, while the elimination method relies on adding or subtracting the equations to remove one variable, simplifying the process of finding the solution.

Transcript

00:01 In this problem, we're trying to find the price of a junior roast beef sandwich from arby's and the big montana sandwich from arby's.

00:10 For this, because we are trying to find two different variables, we're going to let x be our junior roast beef and y is going to be the big montana.

00:20 We are told that 15 roast beef sandwiches, so 15x plus 10.

00:32 Big montana sandwiches equaled a total of $75 .25.

00:40 So we're going to let our first equation be 15x plus 10y equals 7525.

00:46 Our second equation is when we sell 30 roast beef sandwiches and five big montana sandwiches, and that equaled a total of $84 .65.

00:59 Cents so we're going to use those two equations to find out the price of both so let's start let's start we're going to use this second equation and we're going to solve for y in this equation so i'm going to start by subtracting 30x on both sides i'm going to get 5y equals negative 30x plus 8465 i'm going to divide by 5 and i'm going to divide each thing by five and when i do i'm left with y equals negative six x plus 16 dollars and 93 cents now we know that y equals this we're going to go back to the first equation and in place of why we're going to put that so we're going to have 15x plus 10 and in place of y we're going to put negative 6x plus 16 dollars 93 cents equals 75 dollars 25 cents and we're going to solve this to find out what x would equal so 15x we're going to do distributed property so we're going to have negative 60x plus 169 dollars 30 cents will equal 75 dollars 25 cents we're going to combine 15x and negative 60x so we're really going to have negative 45x plus 169 30 equals 7525.

02:51 We're going to subtract 169 .30 from both sides...

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