Solve the following problem by defining your variables and writing a system of equations: The cost of 8 donuts and 2 bags of coffee is $18. The cost of 3 donuts and 1 bag of coffee is $7.50. How much do 1 donut and 1 bag of coffee cost?

Show your work.

1 donut and a bag of coffee costs $4.50

Step-by-step explanation:

Start by creating a pair of simultaneous equations.

Let a donut.

Let a bag of coffee.

Therefore:

There are a few ways to solve these equations. This time I'll show you the elimination method. We eliminate one of the variables to get the other variable equal to a number.

Start by multiplying one of the equations by a number so that one of the variables has the same coefficient (number at the front) as the same variable in the other equation.

I'll multiply the second equation by 2 so that the will have a coefficient of 2 like the 1st equation.

, .

Now we have two equations with the same coefficient of . We can subtract the equations from each other to eliminate the variable and leave equal to a number.

Subtracting   and :

Simplify to get .

Therefore .

Now we have one of the variables, we can find the other variable by putting the known variable back into one of the equations.

- original equation

- substituting .

- simplifying

- re-arranging to solve for

Therefore, and .

So 1 donut costs $1.50 and 1 bag of coffee costs $3.

1 donut and a bag of coffee costs $4.50

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step-by-step explanation: