Tickets to a museum cost $3 and $8 for adults. a group of four visitors to the museum spent a total of $22 on tickets. Write and solve a system of equations to represent this situation. Interpret the solution
Ur dum
Let's represent the number of tickets for adults as "x" and the number of tickets for other visitors as "y".
From the given information, we know that the cost of an adult ticket is $8, so the total cost of adult tickets can be represented as 8x. Similarly, the cost of a ticket for other visitors is $3, so the total cost of tickets for other visitors can be represented as 3y.
We also know that the group of four visitors spent a total of $22 on tickets. Therefore, the total cost can be represented as 22.
Now we can write the system of equations:
1. The total number of tickets is 4: x + y = 4
2. The total cost of the tickets is $22: 8x + 3y = 22
To solve this system of equations, we can use the substitution method or the elimination method.
Let's use the substitution method:
From equation 1, we can express x in terms of y: x = 4 - y
Substituting this value of x into equation 2, we get: 8(4 - y) + 3y = 22
Simplifying the equation: 32 - 8y + 3y = 22
Combining like terms: -5y = -10
Dividing by -5: y = 2
Now we can find x by substituting the value of y back into equation 1: x + 2 = 4
Subtracting 2 from both sides: x = 2
The solution to the system of equations is x = 2 and y = 2.
Interpreting the solution: There were 2 adult tickets sold and 2 tickets sold for other visitors.
Let's represent the number of adult tickets as 'x' and the number of regular tickets as 'y'.
We know that the cost of an adult ticket is $8 and the cost of a regular ticket is $3.
So, for the group of four visitors, we can set up the following equations:
Equation 1: x + y = 4 (since there are four visitors in total)
Equation 2: 8x + 3y = 22 (since the total cost of tickets is $22)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method here:
From Equation 1, we can isolate one variable (let's choose x) and rewrite it as x = 4 - y.
Now, we substitute this value of x in Equation 2:
8(4 - y) + 3y = 22
32 - 8y + 3y = 22
-5y = 22 - 32
-5y = -10
Dividing both sides of the equation by -5, we get:
y = 2
Substituting the value of y back into Equation 1:
x + 2 = 4
x = 4 - 2
x = 2
So, the solution to the system of equations is x = 2 and y = 2.
Interpreting the solution, we conclude that there were 2 adult tickets and 2 regular tickets purchased.
Number of $3 tickets ---- x
number of $8 tickets ---- 4-x
3x + 8(4-x) = 22
solve for x and interpret
or
Number of $3 tickets ---- x
number of $8 tickets ---- y
then
x+y = 4
3x + 8y = 22
solve for x and y and interpret