Question

Three jelly donuts and two glazed donuts cost $1.30. One jelly donuts cost .10 less than two glazed donuts. What are the cost of one jelly doughnut in the cost of one glazed donut?

Answer 1

Three jelly donuts and two glazed donuts cost $1.30. Thefore we can write the equation

`3x+2y=1.3`

Where "x" is the cost of one jelly donut and y is the cost of one glazed donut.

And one jelly donuts cost .10 less than two glazed donuts. Then we can write the second equation

`x=2y-0.1`

We can write that equation as

`x-2y=-0.1`

Now we have a system of equations

`\begin{cases}3x+2y=1.3 \\ x-2y=-0.1\end{cases}`

If we sum them we get

`\begin{gathered} 3x+x+2y-2y=1.3-0.1 \\ \\ 4x=1.2 \\ \\ x=(1.2)/(4) \\ \\ x=0.3 \end{gathered}`

Now we have the value of x we can put it in one of our equations and solve for y

`\begin{gathered} 0.3-2y=-0.1 \\ \\ 2y=0.4 \\ \\ y=0.2 \end{gathered}`

Therefore

`\begin{gathered} x=0.3 \\ y=0.2 \end{gathered}`

The cost of one jelly doughnut is $0.3 and the cost of one glazed donut is $0.2