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

Step-by-step 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.

$\qquad❖ \: \sf \:6x + 3y = 26.70$

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

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

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

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

$\qquad❖ \: \sf \:21x =67 .20$

$\qquad❖ \: \sf \:x = 67.20 \div 21$

$\qquad❖ \: \sf \:x = 3.20$

So, cost of each burger is x = $ 3.20

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

Therefore, cost of two burgers is :

• 2 × 3.20 = $ 6.40