Question

PLEASE ANSWER :) !!!!!!!!!!!!!!!!!!!!!!

1. Which number is NOT the sum of three consecutive integers?

a. 65

b. 150

c. 42

d. 57


2. Train A leaves a station traveling at 48 kilometers per hour. Four hours later, Train B leaves the same station traveling in the same direction at 68 kilometers per hour. What equation can you use to find the time t in hours that it took train B to catch up with Train A, and what is the value of t?

a. 68(t – 4) = 48t; t = 13.6 hours

b. 48(t + 4) = 68t; t = 10.6 hours

c. 68(t + 4) = 48t; t = –9.6 hours

d. 48(t + 4) = 68t; t = 9.6 hours


3. The sum of two consecutive integers is –27. If n represents one of the integers, what equation can you write to find the value of the two integers and what are the integers?

a. n + (n – 1) = –27; –14 and –15

b. n + (n + 1) = –27; –14 and –12

c. n + (n + 1) = –27; –14 and –13

d. n + (n + 1) = –27; –14 and –15


4. The length of a rectangle is one fourth its width. The perimeter of the rectangle is 60 centimeters. If w represents the width of this rectangle, which expression represents its length?

a. l = 1 over 4w

b. l = 4w

c. l = 60 – w

d. l = 60 – 2w

Answer 1

1. A

2. A

3. C

4. A

Explanation:

1. Three consecutive integers are represented as n, n+1, and n+2. The sum

n+(n+1)+(n+2) = # must be only true using integers (no fractions/decimals).

So try the first answer 65.

n+(n+1)+(n+2) =65

3n+3=65

3n=62

n=62/3

n=20.6666666666666....

This is not an integer so A is the solution.

2. The first train arrives at 48t since it travels 48 km per hour for t hours.

The second train is 68(t-4) since it travels 68 km per hour for the same t hours minus 4 (it left 4 hours later). The time they reach each other is when they are equal. So 68(t-4)=48t or answer A.

3. Two consecutive integers are represented as n and n+1. Notice when added they must equal -27. The only answer option that works is -14 + -13 = -27. Answer C is the solution.

4. The length is one fourth of its width is multiplication by 1/4. So l = 1/4 w or answer A is the solution.