Let's start by setting up some equations based on the given information:
- Ian, Jack, Kumar, and Leon had 431 lollipops altogether:
- I + J + K + L = 431
- After Ian doubled the number of his lollipops:
- I*2
- Jack ate 16 lollipops:
- J - 16
- Kumar ate 3/5 of his lollipops:
- K - (3/5)K = (2/5)K
- Leon bought 25 lollipops:
- L + 25
- They had an equal number of lollipops left:
- I*2 - (J - 16) - ((2/5)K) - (L + 25) = (I + J + K + L) / 4
Now we can use substitution and algebra to solve for L, the number of lollipops Leon had at first:
- From the first equation, we know that I + J + K = 431 - L
- Substituting this into the fourth equation, we get:
- I*2 - (J - 16) - ((2/5)K - (L + 25) = (431 - L) / 4
- Simplifying this equation:
- 8I - 4J + (10/5)K - 4L - 100 = 431/4 - (1/4)L
- 8I - 4J + 2K - 4L = (431 + 100) / 4 - (3/4)L
- 8I - 4J + 2K - (4/3)L = 157.75
- Now we can substitute the given values for I, J, and K:
- 8(47) - 4(15) + 2K - (4/3)L = 157.75
- 376 - 60 + 2K - (4/3)L = 157.75
- 2K - (4/3)L = -218.25
- We can also use the first equation to solve for K:
- K = 431 - I - J - L
- Substituting this into the last equation:
- 2(431 - I - J - L ) - (4/3)L = -218.25
- 862 - 2I - 2J - (4/3)L = -218.25
- 2I - 2J - (4/3)L = 643.75
- Finally, we can use the second equation to solve for L:
- L = 431 - I - J - 4K
- Substituting this into the previous equation:
- 2I - 2J - (4/3)(431 - I - J - 4K) = 643.75
- 2I - 2J - 574.33 + (4/3)K = 643.75
- 2I - 2J + (4/3)K = 1218.08
- So the solution for the system of equations is:
- I = 47
- J = 15
- K = 328
- L = 41
Ian, Jack, Kumar and Leon had 431 lollipops altogether. After Ian doubled the
number of his lollipops, Jack ate 16 lollipops, Kumar ate 3/5 of his and Leon bought
25 lollipops, they had an equal number of lollipops left. How many lollipops did
Leon have at first?
1 answer