Question

1. Three jelly donuts and two glazed donuts cost $1.30. One jelly donut costs $ 0.10 lessthan two glazed doughnuts. What is the cost of one jelly doughnut and the cost ofone glazed doughnut?

Answer 1

To solve the cost of one jelly and one glazed doughnut, we set up a system of linear equations with the given information. Solving the equations, we found that one jelly doughnut costs $0.30 and one glazed doughnut costs $0.20.

Step-by-step explanation:

Understanding the Cost of Doughnuts

We're given a scenario involving the cost of jelly and glazed doughnuts. The problem states that three jelly doughnuts and two glazed doughnuts together cost $1.30. Also, it's mentioned that one jelly doughnut costs $0.10 less than two glazed doughnuts. To find the cost of each doughnut, we can set up a system of equations.

Let's define our variables:

Let g represent the cost of one glazed doughnut

8g - $0.30 = $1.30

j = $0.40 - $0.10

j = $0.30

Therefore, the cost of one jelly doughnut is $0.30 and the cost of one glazed doughnut is $0.20.

Answer 2

The first step to solve the present question is to write the sentences in math form.

The first becomes the following:

`3J+2G=1.30`

where J stands for the value of a single jelly donut while G is the value of one glazed donut. Following this we now write the second sentence:

`J=2G-0.10`

Now, we can substitute the expression we found in the second sentence for the value of J into the first equation. This will allow us to determine the value of a single glazed donut.

`\begin{gathered} 3(2G-0.10)+2G=1.30 \\ 6G-0.30+2G=1.30 \\ 8G=1.30+0.30=1.60 \\ G=(1.60)/(8)=0.20 \end{gathered}`

From the above-developed solution, we are able to say that the price for a single glazed donut is:

G = $ 0.20

Now, we can substitute this value into the second equation to find the value for a single jelly donut, just as follows:

`\begin{gathered} J=2*0.20-0.10 \\ J=0.40-0.10 \\ J=0.30 \end{gathered}`

Now, we are able to conclude that the price for a single Jelly donut is:

J = $ 0.30