Answer:
8 drinks were purchased.
Explanation:
We can use two equations to describe this problem. Then we solve a system of equations in two variables to find the solution.
1) number of items
Let h = number of hamburgers
Let d = number of drinks
Sum of the number of items bought is h + d.
We are told 10 items in total were bought, so h + d = 10
That is our first equation.
2) cost of items
One hamburger costs $4; h hamburgers cost 4h.
One drink costs $2; d drinks cost 2d.
The sum of the costs of the hamburgers and drinks is 4h + 2d.
We are told the total cost is $24, so 4h + 2d = 24. That is our second equation.
We have a system of equations:
h + d = 10
4h + 2d = 24
We will now solve the system of equations using the substitution method.
Solve the first equation for h.
h + d = 10
h = 10 - d
Now substitute 10 - d for h in the second equation.
4h + 2d = 24
4(10 - d) + 2d = 24
Now we have one equation in one variable, so we can solve for d.
40 - 4d + 2d = 24
40 - 2d = 24
-2d = -16
d = 8
8 drinks were purchased.