Answer: B
Step-by-step explanation:
What we know:
- Donovan's height can be expressed through the equation H = 105 + 4.25(a - 5) where H is height and a is age
- Margaret's height is expressed through a given table
How to solve:
We need to create a table for Donovan's height, compare it to Margaret's table, and then choose the appropriate statement. H will represent height, and a will represent age. B and c are constant values, and x is a coefficient to a-c
Process:
Part 1 - Data
Simplifying equation
Set up equation H = 105 + 4.25(a - 5)
Distribute H = 105 + (4.25a - 21.25)
Age 5
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*5) - 21.25]
Simplify H = 105 + (21.25 - 21.25)
Simplify H = 105
Age 6
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*6) - 21.25]
Simplify H = 105 + (25.5 - 21.25 )
Subtract H = 105 + 4.25
Solve H = 109.25
Age 7
Set up equation H = 105 + (4.25a - 21.25)
Substitute H = 105 + [(4.25*7) - 21.25]
Simplify H = 105 + (29.75 - 21.25)
Subtract H = 105 + 8.5
Solve H = 113.5
Continue for the following ages (8-10)
Part 2 - Table Comparison
1. Create a table for both sets of data. Example:
______________________________________________
Age | 5 | 6 | 7 | 8 | 9 | 10 |
Mar. height (cm) | 101 | 105 | 109 | 113 | 117 | 121 |
Don. height (cm) | 105 | 109.25 | 113.5 | 117.75 | 122 | 126. 25 |
______________________________________________
2. Find which statement applies
2a. Margaret did not grow faster than Donovan
2b. Donovan did grow faster than Margaret
2c. Margaret and Donovan did not grow at the same rate
2d. There is enough data to draw a conclusion
Solution: B
Check:
We came to this conclusion by putting Donovan's data into a chart. We can check by writing an equation for Margaret's height. Then, use that equation with Donovan's to see the difference
Margaret's equation:
H = 4a + 81
Comparison (using ages 8 & 9):
8:
H= 4a + 81 | H = 105 + (4.25a - 21.25)
H = (4*8) + 81 | H = 105 + [(4.25*8) - 21.25)
H = 32 + 81 | H = 105 + 12.75
H = 113 | H = 117.75
9:
H = 117 | H = 122
________________________
113 < 117.75
117 < 122
Because the statement still holds true, answer B is correct.