Jake was 4 1/2 feet tall on his 12th birthday, when he began to have

Green2k1

I also had the same dilemma but the question says how many inches per year did Jake grow during his growth spurt? (12 inches = 1 foot)

So, it translates to a constant rate in terms of number of inches increase per year and not to a constant rate in terms of percentages.

I hope I am correct.

rocky620
i am not much concern about this particular question but mainly i have asked from concept clarification view point. And my question is related to bold face section.

Jake was 4 1/2 feet tall on his 12th birthday, when he began to have a growth spurt. Between his 12th and 15th birthdays, he grew at a constant rate. If Jake was 20% taller on his 15th birthday than on his 13th birthday, how many inches per year did Jake grow during his growth spurt? (12 inches = 1 foot)[/b]


Although @buniel has not posted this question, hope he will resolve this doubt..

I used a different approach from the one that Ian used.

The word constant in the question jumps out at me.
If the growth is constant, it must be a straight line and we can form a straight line equation.

Let there be 3 points, where x coordinate represents the age and y coordinate represents the height:
Point A : (12, 54) ............ {As 4 1/2 feet is 54 inches}
Point B : (13, a)
Point C : (15, 1.2a) ............. Given in the question that height at age 15 is 20% higher than age 13, hence 1.2 times.

Now using point B and C to form a straight line equation {y-y1=\(\frac{y2-y1}{x2-x1}\) * (x-x1) }

So y-a=\(\frac{1.2a-a}{15-13}\)*(x-13)

Solving the above we get, 10y+3a=ax

Substituting values of point A(12,54) for x,y in the above we get,

a=60.

At age 15, height is 1.2a=1.2*60=72

Growth per year=\(\frac{Height at 15-Height at 12}{3}\)
=\(\frac{72-60}{3}\)=6 inches

Hence Ans is C

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