The softball team is hosting a dance as a fundraiser. They sold 38 more individual tickets than couples’ tickets and earned a total of $730. Write and solve a system of equations to represent this situation if individual tickets cost $3 and couples’ tickets cost $5. How many individual tickets were sold?How many couples’ tickets were sold?
couple tickets =====> x
solo tickets =====> x + 38
5x + 3(x+38) = 730
solve for x
or, if you insist on using 2 variables ....
couple tickets =====> x
solo tickets =====> y
y - x = 38
3y + 5x = 730
multiply the first by 5, then add them, etc
Let's represent the number of individual tickets sold as "I" and the number of couples' tickets sold as "C".
According to the problem, the softball team sold 38 more individual tickets than couples' tickets, so we can write the first equation as:
I = C + 38
The total amount earned from selling individual tickets is equal to the individual ticket price multiplied by the number of individual tickets sold, which can be written as:
3I
Similarly, the total amount earned from selling couples' tickets is equal to the couple ticket price multiplied by the number of couples' tickets sold, which can be written as:
5C
According to the problem, the total amount earned is $730, so we can write the second equation as:
3I + 5C = 730
Now, we have a system of equations:
I = C + 38
3I + 5C = 730
To solve the system of equations, we can substitute the value of I from the first equation into the second equation:
3(C + 38) + 5C = 730
3C + 114 + 5C = 730
8C + 114 = 730
8C = 730 - 114
8C = 616
C = 616 / 8
C ≈ 77
Substituting this value back into the first equation to find I:
I = 77 + 38
I ≈ 115
Therefore, 115 individual tickets were sold and 77 couples' tickets were sold.
To solve this problem, we can set up a system of equations based on the given information.
Let's assign variables to the unknown quantities:
Let x be the number of couples' tickets sold.
Let x + 38 be the number of individual tickets sold.
The total revenue earned is $730, so we can write the first equation:
5x + 3(x + 38) = 730
To solve this equation, we can simplify and then solve for x:
5x + 3x + 114 = 730
8x + 114 = 730
8x = 730 - 114
8x = 616
x = 616 / 8
x = 77
So, 77 couples' tickets were sold.
To find the number of individual tickets sold, we can substitute the value of x back into our equation:
x + 38 = 77 + 38 = 115
Therefore, 115 individual tickets were sold.
In conclusion, 115 individual tickets were sold and 77 couples' tickets were sold.