A vendor at a craft show sold items for $4.50, $6.00, and $7.50. Altogether, the vendor sold 87 items for a total of $489. The vendor
sold five more items for $6.00 than for $7.50.

Let x = number of $4.50 craft items sold
Let y = number of $6.00 craft items sold
Let z = number of $7.50 craft items sold

Which system of equations could you use to determine how many
of each item were sold?

x + y + z = 489
z = y + 5
4.5x + 6y + 7.5z = 87

x + y + z = 87
y = z + 5
4.5x + 6y + 7.5z = 489

x + y + z = 489
y = z + 5
4.5x + 6y + 7.5z = 87

x + y + z = 87
z = y + 5
4.5x + 6y + 7.5z = 489

You could either use the second or fourth system as each of these choices have x+y+z=87 in the first equation.

Step-by-step explanation:

Answer(s) is above. Hope it helps!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240