Question

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.

Answer 1

Answer:

1 donut and a bag of coffee costs $4.50

Step-by-step explanation:

Start by creating a pair of simultaneous equations.

Let $x =$ a donut.

Let $y =$ a bag of coffee.

Therefore:

$8x+2y=18$

$3x+y=7.50$

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 $y$ will have a coefficient of 2 like the 1st equation.

$2(3x+y)=2(7.50)$, $6x+2y=15$.

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

Subtracting  $8x+2y=18$ and $6x+2y=15$ :

$8x+2y-(6x+2y)=18-(15)$

Simplify to get $2x=3$.

Therefore $x = 1.5$.

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

$3x+y=7.50$ - original equation

$3(1.50)+y=7.50$ - substituting $x$.

$4.50 +y=7.50$ - simplifying

$y=3$ - re-arranging to solve for $y$

Therefore, $x=1.5$ and $y=3$.

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

1 donut and a bag of coffee costs $4.50