Problem
of the Week
Problem
B and Solution
Line
Up These Letters!

Problem

Determine the number corresponding to each letter so that the two
number lines in each box have the same range. The first letter has been
done for you.

The top number line goes from \(1.2\) to \(6.7\) and the bottom number line goes from
\(10.3\) to \(I\) where \(I =
15.8\).

The top number line goes from \(20.6\) to \(39.1\) and the bottom number line goes from
\(4\) to \(M\).

The top number line goes from \(16.9\) to \(32\) and the bottom number line goes from
\(L\) to \(50\).

The top number line goes from \(12.09\) to \(13.01\) and the bottom number line goes
from \(3.01\) to \(E\).

The top number line goes from \(17.6\) to \(36.25\) and the bottom number line goes
from \(C\) to \(23.3\).

The top number line goes from \(15.5\) to \(36.05\) and the bottom number line goes
from \(3.67\) to \(A\).

The top number line goes from \(3.1\) to \(7.3\) and the bottom number line goes from
\(D\) to \(6.1\).

Then write the numbers in the table below, in order from
least to greatest, along with their corresponding letters in the row
below. The corresponding letters will spell a mathematical term!

Numbers

\(15.8\)

Letters

\(I\)

Solution

In each case, the range of the number line with the given end points
must first be determined. These are shown above the top number line in
each box. For example, the range of the number line in the first box is
\(6.7-1.2=5.5\).

Then the unknown endpoint on the bottom number line can be determined
by either addition or subtraction. For example, in the first box, \(I = 10.3+5.5=15.8\).

The calculations for each box are shown in the following diagram.

The top number line goes from \(1.2\) to \(6.7\) with a range of \(5.5\). The bottom number line goes from
\(10.3\) to \(I\) where \(I =
10.3 + 5.5 = 15.8\).

The top number line goes from \(20.6\) to \(39.1\) with a range of \(18.5\). The bottom number line goes from
\(4\) to \(M\) where \(M =
4+18.5 = 22.5\).

The top number line goes from \(16.9\) to \(32\) with a range of \(15.1\). The bottom number line goes from
\(L\) to \(50\) where \(L =
50 - 15.1 = 34.9\).

The top number line goes from \(12.09\) to \(13.01\) with a range of \(0.92\). The bottom number line goes from
\(3.01\) to \(E\) where \(E =
3.01 + 0.92 = 3.93\).

The top number line goes from \(17.6\) to \(36.25\) with a range of \(18.65\). The bottom number line goes from
\(C\) to \(23.3\) where \(C
= 23.3 - 18.65 = 4.65\).

The top number line goes from \(15.5\) to \(36.05\) with a range of \(20.55\). The bottom number line goes from
\(3.67\) to \(A\) where \(A =
3.67 + 20.55 = 24.22\).

The top number line goes from \(3.1\) to \(7.3\) with a range of \(4.2\). The bottom number line goes from
\(D\) to \(6.1\) where \(D =
6.1 - 4.2 = 1.9\).

When the numbers are written in order from least to
greatest, along with their corresponding letters, the letters spell the
word DECIMAL, as shown.