Answer :
To find the allowable weight for a female 5 foot 9 inch mission specialist, let's go through the problem step by step.
1. Starting Weight Allowance:
For the first 5 feet, the allowed weight is given as 101 pounds.
2. Height Over 5 Feet:
The mission specialist is 5 feet 9 inches tall. Therefore, the additional height over 5 feet is 9 inches.
3. Weight Allowance for Additional Inches:
For every additional inch over the initial 5 feet, the allowed weight increases by 5 pounds per inch.
4. Calculate Additional Weight:
To calculate the additional weight for the 9 inches over 5 feet:
[tex]\[
\text{Additional weight} = 9 \, \text{inches} \times 5 \, \text{pounds/inch} = 45 \, \text{pounds}
\][/tex]
5. Total Allowable Weight:
The total allowed weight is the sum of the initial weight for the first 5 feet and the additional weight for the 9 inches:
[tex]\[
\text{Total allowable weight} = 101 \, \text{pounds} + 45 \, \text{pounds} = 146 \, \text{pounds}
\][/tex]
6. Inequality Representation:
If [tex]\( w \)[/tex] represents the astronaut's weight in pounds, then the inequality representing the allowable weight is:
[tex]\[
w \leq 146
\][/tex]
So, the allowable weight for a female 5 foot 9 inch mission specialist is 146 pounds, and this is represented by the inequality [tex]\( w \leq 146 \)[/tex].
1. Starting Weight Allowance:
For the first 5 feet, the allowed weight is given as 101 pounds.
2. Height Over 5 Feet:
The mission specialist is 5 feet 9 inches tall. Therefore, the additional height over 5 feet is 9 inches.
3. Weight Allowance for Additional Inches:
For every additional inch over the initial 5 feet, the allowed weight increases by 5 pounds per inch.
4. Calculate Additional Weight:
To calculate the additional weight for the 9 inches over 5 feet:
[tex]\[
\text{Additional weight} = 9 \, \text{inches} \times 5 \, \text{pounds/inch} = 45 \, \text{pounds}
\][/tex]
5. Total Allowable Weight:
The total allowed weight is the sum of the initial weight for the first 5 feet and the additional weight for the 9 inches:
[tex]\[
\text{Total allowable weight} = 101 \, \text{pounds} + 45 \, \text{pounds} = 146 \, \text{pounds}
\][/tex]
6. Inequality Representation:
If [tex]\( w \)[/tex] represents the astronaut's weight in pounds, then the inequality representing the allowable weight is:
[tex]\[
w \leq 146
\][/tex]
So, the allowable weight for a female 5 foot 9 inch mission specialist is 146 pounds, and this is represented by the inequality [tex]\( w \leq 146 \)[/tex].
