Question

Mario and Luigi had a 5-day shopping spree. Here's how they spent their money: Mario: $\bullet$ Mario spent $3 on the first day. $\bullet $ Mario spent half his remaining money on the second day. $\bullet$ Mario spent $3 on the third day. $\bullet$ Mario spent half his remaining money on the fourth day. $\bullet$ Mario spent $3 on the fifth day. Luigi: $\bullet$ Luigi spent two-thirds of his money on the first day. $\bullet$ Luigi spent $1 on the second day. $\bullet$ Luigi spent two-thirds of his remaining money on the third day. $\bullet$ Luigi spent $1 on the fourth day. $\bullet$ Luigi spent one-half of his remaining money on the fifth day. Mario ran out of money after the fifth day, so they both stopped shopping. If Mario and Luigi had the same amount of money at the end of the second day, how much money did Luigi start with?

Answer 1

Let the amount of money that Mario started with = M
What Mario was left with after 1st day = M - 3
What Mario was left with after 2nd day = 1/2 [ M - 3 ] = 1/2M - 1.5
What Mario was left with after 3rd day = 1/2M - 1.5 - 3 = 1/2M - 4.5

What Mario was left with after 4th day = 1/2 [ 1/2M - 4.5 ] = 1/4M - 2.25
What Mario was left with after 5 days = 1/4M - 2.25 - 3 = 1/4M - 5.25

Let the amount of money that Luigi started with = L
What Luigi was left with after 1st day = 1/3L

What Luigi was left with after 2nd day = 1/3L - 1

Now we have,
1/4M - 5.25 = 0
1/2M - 1.5 = 1/3L - 1
Solving these equations
1/4M = 5.25
M = 21
Putting in 2nd equation, we get
1/2 (21) - 1.5 = 1/3 L - 1
10.5 - 1.5 + 1 = 1/3 L
10 = 1/3 L
L = 30
Therefore, Luigi started with $30.