Question

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Answer 1

Answer:yes

Explanation:

Answer 2

There are two families who visit a park and pay the entrance fee. The distribution of each family and the total cost paid at the entrance by each are given:

Family 1:

`\begin{gathered} NumberofAdults(A_1\text{ )= 2} \\ NumberofChildren(B_{1\text{ }})\text{ = 3} \\ TotalEntryCost(C_1)\text{= }20\text{ pounds} \end{gathered}`

Family 2:

`\begin{gathered} NumberofAdults(A_2\text{ ) = 1} \\ NumberofChildren(B_2\text{ )= 4} \\ TotalEntryCost(C_2\text{ )= 15 pounds} \end{gathered}`

Now we will define the ticket rates for adults and children at this park:

`\begin{gathered} \text{Adult Rate = x} \\ \text{Children Rate = y} \end{gathered}`

Next step is to express the total entry cost born by each family. This is done by multiplying the rate of each age group with the respective distribution of age group comprising each family.

Family 1:

`\begin{gathered} C_1\text{ = x}\cdot A_1\text{ + y}\cdot B_1 \\ 20\text{ = 2}x\text{ + 3}y\text{ }\ldots.\text{ Eq1} \end{gathered}`

Family 2:

`\begin{gathered} C_2\text{ = x}\cdot A_2\text{ + y}\cdot B_2 \\ 15\text{ = x + 4y }\ldots Eq\text{ 2} \end{gathered}`

We have two equation with two unknowns representing the cost charged for adults ( x ) and cost charged for children ( y ) at the park entrance.

We will solve the equation simultaneously ( Eq1 and Eq2 ) by using the process of Elimination:

`\begin{gathered} 20\text{ = 2x + 3y} \\ -2\cdot(15\text{ = x + 4y) = -30 = -2x -8y} \end{gathered}`
`\begin{gathered} 20\text{ = 2x + 3y} \\ -30\text{ = -2x -8y} \\ ========== \\ -10\text{ = 0 -5y} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}`

Plug the value of ( y ) in either of the two equations and solve for ( x ):

`\begin{gathered} 15\text{ = x + 4(2)} \\ x\text{ = 15 - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7 }} \end{gathered}`

Therefore, the rates charged for each age group are:

`\begin{gathered} \text{\textcolor{#FF7968}{Adult ticket = x = 7 pounds}} \\ \text{\textcolor{#FF7968}{Child ticket = y = 2 pounds}} \end{gathered}`