Question

The mass of each candy in a box is 5g. The mass of the empty box is 20g let T grams represent the total mass of the box and candies. Let n represent the number of candies, so that t= 5n + 20 Using the information create a table of values. And graph the relation. Please help asap!! Thanks

Answer 1

`\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}`

Please refer to graph attached.

Explanation:

Given that mass of each candy in the box is 5 gm.

Mass of empty box is 20 gm.

Total grams,
`T = 5n + 20`

To find: A table of values and graph of the relation.

Solution:

The given equation is nothing but a Linear equation in two variables.

Let us try to create a table of values by putting some values of 'n' and then finding the values for Total grams 'T'.

Let us put
`n = 0 \Rightarrow T =5* 0 +20 = 20`

Let us put
`n = 1 \Rightarrow T =5* 1 +20 = 25`

Let us put
`n = 2 \Rightarrow T =5* 2 +20 = 30`

Let us put
`n = 3 \Rightarrow T =5* 3 +20 = 35`

Let us put
`n = 4 \Rightarrow T =5* 4 +20 = 40`

So, the table of values becomes:

`\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}`

We can see that the value of T is increasing with increasing values of 'n'.

Please refer to the attached image for the graph of given equation.

As it is a linear equation in two variables, it will be a straight line. It will be an increasing positive slope graph.