Astudent 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?

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.

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.