The ratio of grade 7's to grade 8's is 5:3. If there are a total of 90 grade 8's, how many total
students are there in grade 7 and 8?

240 students

Step-by-step explanation:

Grade 7 : Grade 8 = 5 : 3

Number of seventh grade students = 5x

Number of Eighth grade students = 3x

3x = 90

x = 90÷3

x = 30

Total students = 5x + 3x = 8x = 8 * 30 = 240

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(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