the athletic department ordered a total of 29 basketballs and footballs for $1000. if the basketballs cost $30 each and the footballs cost $40 each, how many footballs were purchased?
if there are x footballs, then the rest (29-x) are basketballs. So, just add up the costs:
40x + 30(29-x) = 1000
To find the number of footballs purchased, we can set up a system of equations. Let's denote the number of basketballs as "b" and the number of footballs as "f".
We're given two pieces of information: the total number of basketballs and footballs is 29, and the total cost of the order is $1000.
From the first piece of information, we can write the equation:
b + f = 29
To find a way to express the total cost, let's consider that basketballs cost $30 each and footballs cost $40 each.
So, the total cost of the basketballs (in dollars) would be: 30b.
The total cost of the footballs (in dollars) would be: 40f.
From the second piece of information, we can write the equation:
30b + 40f = 1000
Now, we have a system of equations:
b + f = 29
30b + 40f = 1000
There are several ways to solve this system of equations. One common method is substitution. Let's solve for b in terms of f using the first equation:
b = 29 - f
Substituting this value of b into the second equation, we get:
30(29 - f) + 40f = 1000
Expanding the equation:
870 - 30f + 40f = 1000
Combining like terms:
10f = 1000 - 870
10f = 130
Dividing both sides of the equation by 10:
f = 13
Therefore, the athletic department purchased 13 footballs.