Question

Finn bought a yoyo from a company that claims that, with each retraction, the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times. His data are charted below.

Throw Length of string (feet)
1 3
2 2.4
3 1.92

Finn wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?

A.) 13.39 feet
B.) 15.00 feet
C.) 4.46 feet
D.) 0.40 foot

Answer 1

I'll just have to do manual computation per throw.

1) 3
2) 2.4
3) 1.92
4) 1.92 * 0.80  = 1.536
5) 1.536 * 0.80 = 1.2288
6) 1.2288 * 0.80 = 0.9830
7) 0.9830 * 0.80 = 0.7864
8) 0.7864 * 0.80 = 0.6291
9) 0.6291 * 0.80 = 0.5033
10)0.5033 * 0.80 = 0.4026

sum of all tries is 13.3892 or A) 13.39 feet

Answer 2

The sum of the lengths is 13.39 feet.

Calculation of the sum of the length:

Since  the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times.

So,

= 3 + 2.4 + 1.92 +  80% of 1.92 +  80% of 1.536 +  80% of 1.2288 + 80% of 0.983  + 80% of 0.7864 + 80% of 0.6291 +  80% of 0.5033

= 3 + 2.4 + 1.92 +  1.536 + 1.2288 + 0.9830 + 0.7864 + 0.6291 + 0.5033 + 0.4026

= 13.39 feet

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