ticka05 said:
1. write the numberal in base ten
25 eight
2. convert the base-ten to a numberal in the indicated base.
329 to base six
3.The ratio of staff to patients at Lakeview is 8 to 7. If total staff plus patients is 1575 people how many staff are at lakeview? I have to solve the problem
4. solve the proportion
6/x = 11/x+10
please help.
1. write the numberal in base ten
25 eight
I assume you want to solve
\(\displaystyle 25_8 \, = \, x_{10}\)
I'll do a similar but different problem
\(\displaystyle 531_6 \, = \, (5*6^2 \, + \, 3*6^1 \, + 1*6^0)_{10} \, = (180 \, + \, 18 \, + \, 1)}_{10} = (199)_{10}\)
2. convert the base-ten to a numberal in the indicated base.
199 to base six(
similar but different problem)
\(\displaystyle (199)_{10} \, = \, 5 * 6^2 \, + \, 19 \, = \, 5 * 6^2 \, + \, 3*6 \, + \, 1 = \, (531)_6\)
3.The ratio of staff to patients at Lakeview is 4 to 3. If total staff plus patients is 49 people how many staff are at lakeview? I have to solve the problem (
similar but different problem)
Let
the number staff = S
The number of patients = P
The ratio of staff to patients at Lakeview is 4 to 3
S/P = 4/3
S = 4/3 * P.......................................................(1)
If total staff plus patients is 49 people
S + P = 49........................................................(2)
Using (1) in (2)
4/3*P + P = 49
7/3 * P = 49
P = 21..............................................................(3)
using (3) in (1)
S = 4/3 * P = 4/3 * 21 =
28
Check
S + P = 21 + 28 = 49 ...............checks
4. solve the proportion
\(\displaystyle \frac{5}{x} \, = \, \frac{2}{x-6}\)
Multiply both sides by the lowest-common-multiple (LCM) of the denominators --> x(x-6)
\(\displaystyle \frac{5}{x} \cdot x \cdot (x-6) \, = \, \frac{2}{x-6}\cdot x \cdot (x-6)\)
\(\displaystyle 5 \cdot (x-6) \, = 2 \cdot x\)
\(\displaystyle 5x - 30 \, = 2x\)
\(\displaystyle 3x \, = \, 30\)
\(\displaystyle x = 10\)
check
\(\displaystyle \frac{5}{x} \, = \, \frac{2}{x-6}\)
\(\displaystyle \frac{5}{10} \, = \, \frac{2}{10-6}\)
checks.......
