Question

1. The mean of the data set{9,5,y,2,x} is twice the data set {8,x,4,1,3}. What is (y-x) squared.

2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?

Answer 1

1. (y - x)² = 256

2. 128g needed to be added

Explanation:

1.

9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)

16 + y + x = 32 + 2x

y - x = 16

∴ (y - x)² = 256

2.

x = mass of alcohol to add

480 × 0.24 = 115.2 ← current mass of alcohol

0.4(480 + x) = 115.2 + x (×5)

2(480 + x) = 576 + 5x

960 + 2x = 576 + 5x

3x = 384

x = 128g