Question

The sum of three decimals is 21.7. The greatest decimal is twice the next greatest decimal and 4 times the least decimal. What are the three decimals?
A. 3.1, 6.2, 12.4
B. 3.4, 6.8, 13.6
C. 4.2, 8.4, 16.8
D. 4.3, 8.6, 9.1

Answer 1

Let's define the three decimals based on their relationships:

Let:
- The least decimal = \( x \)
- The next greatest decimal = \( y \)
- The greatest decimal = \( z \)

From the problem, we have the following relationships:

1. \( z = 2y \) (The greatest decimal is twice the next greatest decimal)
2. \( z = 4x \) (The greatest decimal is four times the least decimal)
3. \( x + y + z = 21.7 \) (The sum of the three decimals is 21.7)

Substituting the first two equations into the sum equation:

From \( z = 2y \), we can express \( y \) in terms of \( x \):

1. \( z = 4x \) (from equation 2) implies \( 2y = 4x \), so \( y = 2x \).

Now substitute \( y = 2x \) and \( z = 4x \) into the sum equation:

\[
x + 2x + 4x = 21.7
\]

Combine terms:

\[
7x = 21.7
\]

Now solve for \( x \):

\[
x = \frac{21.7}{7} = 3.1
\]

Now that we have \( x \), we can find \( y \) and \( z \):

\[
y = 2x = 2(3.1) = 6.2
\]
\[
z = 4x = 4(3.1) = 12.4
\]

Thus, the three decimals are:

- Least decimal: \( x = 3.1 \)
- Next greatest decimal: \( y = 6.2 \)
- Greatest decimal: \( z = 12.4 \)

So the answer is:

**A. 3.1, 6.2, 12.4**