the basketball tam sold t-shirts and hats as a fundraiser . they sold 23 items and made a profit of 246$ they made a profit of 10$ for every t-shirt they sold and a profit of 12$ for every hat they sold.
what is the number of t-shirts and the number of hats the team sold
Using two variables:
let the numbers of t-shirts be t
let the number of hats be h
h + t = 23 ------------> 5h + 5t = 115
12h + 10t = 246 ----> 6h + 5t = 123
subtract: h = 8 , sub back into h+t = 23 to get t = 15
Using one variable:
let the number of t-shirts be x
then the number of hats is 23-x
10x + 12(23-x) = 246
10x + 276 -12x = 246
-2x = --30
x = 15
then 23-15 = 8
etc.
same result
Well, let's put on our funny hats and solve this problem! (Yes, I know it's about basketball, but we'll be basketball clowns for a moment.)
Let's assume "t" represents the number of t-shirts sold, and "h" represents the number of hats sold. We know that they sold a total of 23 items, so:
t + h = 23
The profit from selling t-shirts is $10 per shirt, and the profit from selling hats is $12 per hat. We also know the total profit they made was $246, so:
10t + 12h = 246
Now, let's juggle these equations a bit. We can rewrite the first equation as:
t = 23 - h
Now, let's substitute this value of t into the second equation:
10(23 - h) + 12h = 246
Expanding the left side:
230 - 10h + 12h = 246
Combining like terms:
2h = 16
Dividing both sides by 2:
h = 8
So, the team sold 8 hats. Now, let's substitute this value back into the first equation:
t + 8 = 23
Subtracting 8 from both sides:
t = 15
Therefore, the team sold 15 t-shirts and 8 hats to make their fundraising a slam dunk!
Let's assume x represents the number of t-shirts sold and y represents the number of hats sold.
According to the given information, the team sold a total of 23 items. So, we can write an equation based on the number of items sold:
x + y = 23
The team also made a profit of $246. The profit from the t-shirts is $10 for each t-shirt sold and $12 for each hat sold. Therefore, the total profit can be expressed as:
10x + 12y = 246
Now we can solve this system of equations to find the values of x and y.
To find the number of t-shirts and hats the basketball team sold, we can set up a system of equations.
Let's represent the number of t-shirts sold as "x" and the number of hats sold as "y".
According to the given information, the team sold a total of 23 items. So we can write the first equation as:
x + y = 23
We also know that they made a profit of $246. The profit from each t-shirt sold is $10, and the profit from each hat sold is $12. So the second equation can be written as:
10x + 12y = 246
Now we have a system of two equations:
x + y = 23
10x + 12y = 246
To solve this system, we can use substitution or elimination. Let's use elimination to solve for "x" and "y".
Multiply the first equation by -10:
-10(x + y) = -10(23)
-10x - 10y = -230
Now we can add this equation to the second equation:
(-10x - 10y) + (10x + 12y) = -230 + 246
2y = 16
Divide both sides of the equation by 2:
2y/2 = 16/2
y = 8
Now, substitute the value of "y" back into the first equation:
x + 8 = 23
x = 23 - 8
x = 15
Therefore, the team sold 15 t-shirts and 8 hats.