drama club sold adult tickets for $8 and kid tickets for $5. for the final performance a total of 226 tickets were sold for a total of $1670. how many adult tickets were sold for the performance?
X = # of adult tickets
Y = # of kid tickets
X + Y = 226
8X + 5Y = 1670
Solve those two equations in two unknowns. One way would be to use substitution. (Insert 226 - X in place of Y in the second equation).
Let x = adult's tickets
y = children's tickets
Equation Insert x value in
1. x + y = 226 first equation
180 + y=226
2. 8x + 5y = 1670 y=226-180
By substitution, y=46
x=180,y=46 Ans.
y = 226-226-x
2. 8x + 5(226-x)=1670 multiply
8x + 1130 - 5x=1670 cancellation
8x-5x=1670-1130
3x=540
x=180 continue above:
Let x = adult's tickets
y = children's tickets
Equation Insert x value in
1. x + y = 226 first equation
180 + y=226
2. 8x + 5y = 1670 y=226-180
By substitution, y=46
x=180,y=46 Ans.
y = 226-226-x
2. 8x + 5(226-x)=1670 multiply
8x + 1130 - 5x=1670 cancellation
8x-5x=1670-1130
3x=540 divide
x=180 continue above:
Using substitution:
X + (226 - X) = 226
8X + 5(226 - X) = 1670
Simplify the equations:
226 = 226
8X + 5(226) - 5X = 1670
Combine like terms:
226 = 226
8X + 1130 - 5X = 1670
Combine like terms again:
226 = 226
3X + 1130 = 1670
Subtract 1130 from both sides:
226 - 1130 = 1670 - 1130
-904 = 540
This is not a true statement, so there is no solution to the equations.
Therefore, we cannot determine how many adult tickets were sold for the performance based on the given information.
Let's solve the system of equations using the substitution method.
We have the equations:
X + Y = 226 ...(1)
8X + 5Y = 1670 ...(2)
To solve for X using substitution, we rearrange equation (1) to get Y in terms of X:
Y = 226 - X
Now we substitute Y in equation (2) with its equivalent value:
8X + 5(226 - X) = 1670
Distribute the 5 to each term inside the parentheses:
8X + 1130 - 5X = 1670
Combine like terms:
3X + 1130 = 1670
Next, isolate the term with X by subtracting 1130 from both sides:
3X = 1670 - 1130
3X = 540
Finally, divide both sides by 3 to solve for X:
X = 540 / 3
X = 180
Therefore, 180 adult tickets were sold for the performance.