Respuesta :
Answer:
$12 for senior citizen tickets and $13 for child tickets
Step-by-step explanation:
To find the prices for senior citizen and child tickets for Mofor's school, it's best to assign variables to each ticket type and create a systems of equations to find out how much each ticket costs.
Let's assign a variable for each ticket type:
- [tex]x[/tex] for senior citizen tickets
- [tex]y[/tex] for child tickets
On the first day of sales, 9 senior citizen and 14 child tickets were sold for a total of 290 dollars.
- We can use this information and our variables to construct our first equation: [tex]9x+14y=290[/tex] .
On the second day of sales, 5 senior citizen and 7 child tickets were sold for a total of 151 dollars.
- Let's repeat the previous step that was done to create our second equation: [tex]5x+7y=151[/tex] .
To find the values of x and y, we can solve it by elimination or substitution.
- For elimination, you can multiply or divide a whole equation and eliminate a variable with the same opposing coefficients so you can find the other variable and plug in that value to find the variable you cancelled out.
- For substitution, you can make one formula from a system equal to one variable to plug it into the second equation to find the value of a variable. Then proceed by plugging in this value to an equation to find the other variable.
Either methods are sufficient and some methods can work more easier than others, but both should lead to the same answer when done correctly. The work would be shown using the elimination method, as substituting would produce fractions which could be avoided.
Given: [tex]9x+14y=290[/tex]
[tex]5x+7y=151[/tex]
Multiply the second equation by -2 to cancel out 14y.
[tex]-2(5x+7y=151)[/tex]
Distribute the number to each term.
[tex]-10x-14y=-302[/tex]
Using our new equation, let's add it to the first equation.
[tex]9x+14y-10x-16y=290-302[/tex]
Combine like terms.
[tex]-x=-12[/tex]
[tex]x=12[/tex]
By finding that x=12, it is understood that senior citizen tickets costs 12 dollars each. By using this value and plugging it into an equation, we are able to find the price for a child ticket.
Let's use the first equation.
Given: [tex]9x+14y=290[/tex]
Plug in [tex]x=12[/tex] into the equation.
[tex]9(12)+14y=290[/tex]
[tex]108+14y=290[/tex]
Isolate the y variable to find the value.
[tex]14y=182\\[/tex]
[tex]y=13[/tex]
By using the process of elimination, we are able to find that the cost for a senior citizen ticket is 13 dollars while a child ticket is 12 dollars.
Let's make sure these two values are correct by plugging them into either initial equation.
[tex]9x+14y=290[/tex]
[tex]9(12)+14(13)=290\\[/tex]
[tex]290=290[/tex]
Therefore, the answer is proven to be correct.
Answer:
Price of a senior citizen ticket = $12
Price of a child ticket = $13
Step-by-step explanation:
Let's denote the price of a senior citizen ticket as [tex]\sf S [/tex] and the price of a child ticket as [tex]\sf C [/tex].
On the first day, the school sold 9 senior citizen tickets and 14 child tickets, totaling $290.
This can be represented by the equation:
[tex]\sf 9S + 14C = 290 [/tex]
On the second day, the school sold 5 senior citizen tickets and 7 child tickets, totaling $151.
This can be represented by the equation:
[tex]\sf 5S + 7C = 151 [/tex]
Now, we have a system of two equations with two unknowns:
[tex]\sf \begin{cases} 9S + 14C = 290 \\ \\ 5S + 7C = 151 \end{cases} [/tex]
We can solve this system of equations to find the values of [tex]\sf S [/tex] and [tex]\sf C [/tex].
One way to solve it is by multiplying the second equation by 2 so that when we add the two equations, the coefficients of [tex]\sf C [/tex] will cancel each other out:
[tex]\sf \begin{cases} 9S + 14C = 290 \\\\ 10S + 14C = 302 \end{cases} [/tex]
Now, subtract the first equation from the second:
[tex]\sf (10S + 14C) - (9S + 14C) = 302 - 290 [/tex]
[tex]\sf S = 12 [/tex]
Now that you have the value of [tex]\sf S [/tex], we can substitute it back into one of the original equations to find [tex]\sf C [/tex]. Let's use the first equation:
[tex]\sf 9S + 14C = 290 [/tex]
[tex]\sf 9(12) + 14C = 290 [/tex]
[tex]\sf 108 + 14C = 290 [/tex]
[tex]\sf 14C = 182 [/tex]
[tex]\sf C = 13 [/tex]
So, the price of a senior citizen ticket ([tex]\sf S [/tex]) is $12, and
the price of a child ticket ([tex]\sf C [/tex]) is $13.
