Kristin's three-year old sister is trying to arrange pink and red starbursts in rows. she has 360 pink starbursts and 150 red starbursts. she wants to arrange them in rows so that there are either only pink or only red starbursts in each row, and so that each row has the same number of starbursts. what is the least number of rows she can make?

17 rows.

Step-by-step explanation:

First we need to find The greatest Common Factor of 360 and 150.

150  = 2 * 3 * 5 * 5

360 = 2 * 2 * 2  * 3 * 3 * 5

So the GCF is 2 * 3 * 5 = 30.

Each row must have 30 Starbursts so the least number of rows

= 150/ 30 = 5 red and 360 / 30 = 12 pink rows.

Total 17 rows.

17 rows

Step-by-step explanation:

360+150=510

360, 150 GCF=30

510/30=17

(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

step-by-step explanation: