Agnes had 4 times as many blue beads as yellow beads. For every 5 beads she used to make a necklace, she used 3 yellow beads. She completed the necklace after she had used up all the yellow beads. If she had 35 blue beads left, how many yellow beads did she have at first?

Answer 1

A bus set off a bus-stop and travelled towards the factory at a constant speed. 20 minutes later, a van set off the same bus-stop and travelled towards the factory along the same route at a constant speed. The van caught up with the bus 40 minutes after leaving the bus-stop. The van's speed was 28 km/h faster than the bus's speed. Find the speed of the van.

Answer 2

Suppose n groups of beads were used for the necklace. Then 3n yellow beads and 2n blue beads were used. So, counting just the blue beads,

35 + 2n = 4*3n

This is not possible if only whole groups of 2 blue and 3 yellow beads were used.

Answer 3

distance = speed * time, so if the van's speed is v, then

v-28 = 2/3 v