Question

1.) Vivian combined different amounts of white paint, blue paint, and green paint to make 145 milliliters (ml) of paint of a new shade. The amount of white paint was x ml. The amount of blue paint was 10 ml less than twice the amount of white paint, and the amount of green paint was half the amount of blue paint. This is represented in the equation below.
x + (2x – 10) + 1/2 (2x – 10) = 145

What was the difference in the amounts of white paint and blue paint Vivian combined?

40 ml
45 ml
30 ml
35 ml


2.) What is the equation of the line that passes through the points (-2, 1) and (1, 10)?

3x - y = 5
x + 3y = -5
3x - y = -5
3x - y = -7

Answer 1

So here are the answers to the given questions above:
1. Since the equation is already given, what we are going to do is to solve for x first. 
x + (2x – 10) + 1/2 (2x – 10) = 145
x + (2x -10) + x - 5 = 145
x + 2x + x - 10 - 5 = 145
4x = 145 +10 + 5
4x = 160 <<divide both sides by 4 and we get
x = 40.
Therefore, the amount of white paint is 40ml.
The amount of blue paint is 70ml and the green paint is 35ml.
So the difference between the amounts of white paint and blue paint Vivian combined is 30ml.
2. The equation of the line that passes through the points (-2, 1) and (1, 10) would be: 3x - y = -7, the last option. In order to check, just plug in the given ordered pairs.