If 132 people attend a concert and tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364, how many of each went to the concert?
__adults
__children

112 adults

20 children

Step-by-step explanation:

In order to solve this problem, we must create system of equations. By definition, system of equations are two equations which help you find unknown variables.

As for this problem, we need to set two variables for each type of person.

Let x represent adults

Let y represent children

We can break the question apart, and form equations based on the information given.

"tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364"

$3.25x + $2.25y = $364

Now, we must form our second equation based on the information given.

"If 132 people attend a concert" "how many of each went to the concert"

x + y = 132

Solve for x, or the total number of adults

x = -y + 132

3.25(-y + 132)+ 2.25y = $364

Distribute 3.25

3.25 * -y = -3.25y

3.25 * 132  = 429

-3.25y + 429 = $364

Subtract 429 from both sides

364 - 429 = -65

-3.25y = -65

Now divide both sides by -3.25 to find the value of y.

y = 20

Therefore, 20 children attended the concert.

In order to find the total amount of adults who attended, subtract 20 from the total number of people that attended.

132 - 20 = 112

So, 112 adults attended as well as 20 children.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet