Question

A student buys a selection of drinks and hamburgers for their friends at a football game. If the student bought 10 items in total for $24 and drinks cost $2 and hamburgers cost $4, how many drinks were purchased?

Answer 1

Answer:

8 drinks were purchased.

Step-by-step 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.