Question

System word problems 1. The cost of 3 boxes of envelopes and 4 boxes of paper is $13.25. 2 boxes of envelopes and 6 boxes of paper cost $17. What is the cost of each?Define Variables:System of Equations:Answer as a sentence:

Answer 1

The cost of a box of envelopes is $1.15

The cost of a box of paper is $2.45

Step-by-step explanation

Define Variables:

Let 'e' represent a box of envelopes

Let 'p' represent a box of papers.

System of Equations:

3e + 4p = 13.25 ...........................(equ 1)

2e + 6p = 17 ...........................(equ 2)

`\begin{gathered} (\text{equ 1) }*-2\Rightarrow-6e\text{ -8p = -26.5 }\ldots\ldots..(equ\text{ 3)} \\ (\text{equ 2) }*3\text{ }\Rightarrow\text{ 6e + 18p = 51 }\ldots\ldots\ldots\ldots..(equ\text{ 4)} \\ \text{ -----------} \\ \text{ 0 e + 10p = 24.5} \\ p\text{ = 2.45} \end{gathered}`
`\begin{gathered} \text{Substitute the value of 'p' into (equ 1)} \\ 3e\text{ + 4p = 13.25} \\ 3e\text{ + 4(2.45) = 13.25} \\ 3e\text{ + 9.8 = 13.25} \\ 3e\text{ = 13.25 - 9.8} \\ 3e\text{ = 3.45} \\ e\text{ = }(3.45)/(3) \\ e\text{ = 1.15} \end{gathered}`

Answer as a sentence

Hence, the cost of a box of envelopes is $1.15 and the cost of a box of paper is $2.45.