EDPT Algebraic Concepts and Equations 5

Question 1

If the ratio of x to y is 3:5 and y = 20, what is x?

Accepted Answer

12

Answer

x/20 = 3/5, so x = 20 × (3/5) = 12.

Question 2

Which expression represents the sum of three consecutive integers starting at n?

Accepted Answer

3n + 3

Answer

n + (n+1) + (n+2) = 3n + 3.

Question 3

If p = 2 and q = -3, what is 3p² - 2q?

Accepted Answer

18

Answer

3(4) - 2(-3) = 12 + 6 = 18.

Question 4

Solve: 2(x - 1) = 3(x + 2)

Accepted Answer

x = -8

Answer

Expanding: 2x - 2 = 3x + 6; subtracting 2x: -2 = x + 6; so x = -8.

Question 5

What is the greatest common factor (GCF) of 12x³ and 18x²?

Accepted Answer

6x²

Answer

GCF of 12 and 18 is 6, and the lowest power of x is x², so GCF = 6x².

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