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?
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.
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.
distance = speed * time, so if the van's speed is v, then
v-28 = 2/3 v
To find out how many yellow beads Agnes had at first, we can set up a proportion using the given information.
Let's say Agnes had y yellow beads at first.
According to the information given, Agnes had 4 times as many blue beads as yellow beads. So, the number of blue beads she had at first is 4y.
Agnes used 5 beads to make a necklace, and out of those 5 beads, 3 were yellow. This means that for every 3 yellow beads used, Agnes used 5 beads in total.
To find the number of yellow beads she used, we can set up the following proportion:
3 yellow beads / 5 total beads = y yellow beads / 4y + 35 remaining beads
Cross-multiplying, we get:
3(4y + 35) = 5y
Now let's solve this equation to find the value of y, which represents the number of yellow beads Agnes had at first.
12y + 105 = 5y
Collecting like terms:
12y - 5y = -105
7y = -105
Dividing both sides by 7:
y = -105 / 7
y = -15
Since the number of beads can't be negative, we can conclude that Agnes had 15 yellow beads at first.