Question

9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.​

Answer 1

Explanation:

Let assume that

Cost of 1 burger = $ x

Cost of 1 doughnuts = $ y

According to statement, 9 burgers and 1 doughnut cost $ 31.30

`\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}`

`\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}`

According to statement again, 3 doughnuts and 6 burgers cost $ 26.70

`\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}`

On substituting the value of y from equation (1), we get

`\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}`

`\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}`

So,

Cost of 2 burgers = 3.2 × 2 = $ 6.4

Answer 2

`\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star`

• 2 burgers cost $ 6.40

`\textsf{ \underline{\underline{Steps to solve the problem} }:}`

We need to make linear equations, to solve this problem.

let the cost of each burger be x, and that of each doughnut be y.

`\qquad❖ \: \sf \:9x + y = 31 .30`

`\qquad❖ \: \sf \:y = (31 . 30 - 9x)`

put value of y in other equation.

`\qquad❖ \: \sf \:6x + 3y = 26.70`

`\qquad❖ \: \sf \:6x + 3(31.3 - 9x) = 26.70`

`\qquad❖ \: \sf \:6x + 93.90 - 27x = 26.70`

`\qquad❖ \: \sf \:6x - 27x = 26.70 - 93.90`

`\qquad❖ \: \sf \:27x - 6x = 93.90 - 26.70`

`\qquad❖ \: \sf \:21x =67 .20`

`\qquad❖ \: \sf \:x = 67.20 / 21`

`\qquad❖ \: \sf \:x = 3.20`

So, cost of each burger is x = $ 3.20

`\qquad \large \sf {Conclusion} :`

Therefore, cost of two burgers is :

• 2 × 3.20 = $ 6.40