Translate to a system of equations and solve. Julia and her...

Translate to a system of equations and solve. Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $\$ 7.80$ per pound with French Roast Columbian coffee that cost $\$ 8.10$ per pound to make a twentypound blend. Their blend should cost them $\$ 7.92$ per pound. How much of each type of coffee should they buy?

Translate to a system of equations and solve.
Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $\$ 7.80$ per pound with French Roast Columbian coffee that cost $\$ 8.10$ per pound to make a twentypound blend. Their blend should cost them $\$ 7.92$ per pound. How much of each type of coffee should they buy?

Key Concepts

Solving Methods for Systems

After establishing the system of equations, solving methods such as substitution or elimination are employed to find the values of the variables. These techniques help simplify and reduce the system to a point where each variable can be isolated and solved, reflecting the underlying relationships defined by the problem.

Translating Word Problems into Equations

This key concept involves converting the narrative or written description of a problem into one or more algebraic equations. It requires identifying the relevant quantities, relationships, and constraints described in the problem and then representing them mathematically, which is essential for creating a system of equations.

System of Linear Equations

A system of linear equations consists of two or more equations with multiple variables that are solved simultaneously. The solution is the set of values for the variables that satisfy all equations at the same time, which is particularly useful for problems involving multiple conditions or constraints.

Mixture Problems

Mixture problems involve combining different components with known properties to create a mixture with a desired characteristic. These problems often require setting up equations based on the total amounts and associated costs or concentrations, allowing one to determine the quantities of each component in the blend.

Transcript

00:01 We're going to turn this into a system of equations and then solve it.

00:04 Julian and her husband own a coffee shop.

00:06 They experiment with mixing a city roast colombian coffee that costs $7 .8 .10 per pound with french roast colombian coffee that costs $8 .10 per pound.

00:16 And they're trying to make a 20 pound blend.

00:19 Their blend should cost them $7 .92 per pound.

00:23 How much of each type of coffee should they buy? so we need to represent both of these two different types with some variable.

00:30 So i'll say pounds of city roast will be c, pounds of french roast will be f.

00:36 We know it's a total of a 20 pound blend right here.

00:40 So that means that if i take c plus f, that's going to be equal to 20 pounds.

00:45 City roast, if we now, for my second equation, i'm going to model the cost.

00:49 So the cost is going to be for city roast is $7 .80 per pound of city roast.

00:56 And we have $8 .10 per pound of french roast.

01:00 And the goal is to get to a cost of $7 .92, but that is going to represent all 20 pounds.

01:07 So we multiply this by 20 for that total cost.

01:09 Okay.

01:11 So we have that right there.

01:12 I'm going to set this up with an elimination...

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