Margaret and Donovan are twins. They have each kept track of their heights every year since they were 5.


Donovan wrote an equation to track his height: h = 105 + 4.25(a - 5)



Based on the evidence shown, which statement correctly compares the twins' rates of growth?

Answer: B

What we know:

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

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)

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

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.

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