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(a) If Keith was tying u balloons, 

3(u -1) + 152 = 7(u -1) + 48

3u – 3 + 152 = 7u – 7 + 48

3u + 149 = 7u + 41

4u = 108

u = 27

There were 27 balloons.

Note: (u – 1) as it needs 2 balloons to have a distance apart. 

(b) 3(26) + 152 = 78 + 152 = 230

The length of the rope is 230 cm. 

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