Question 1184048
he started off with x kg of peanuts.

he ate 1/4 of them last week.


he was left with x = 1/4 * x = 3/4 * x.


he ate 2/3 of the rest last night.


he was left with 3/4 * x - 2/3 * 3/4 * x = 9/12 * x - 6/12 * x = 3/12 * x = 1/4 * x.


his mother gave him another 4.14 kg of peanuts.


he then had as many peanuts as he started with.


1/4 * x + 4.14 kg = x is the equation that models this.


subtract 1/4 * x from both sides of the equation to get:


4.14 = x - 1/4 * x = 3/4 * x.


4.14 = 3/4 * x is the equation after all the arithmetic is done.


multiply both sides of the equation by 4/3 to get:


4.14 * 4/3 = x


solve for x to get:


x = 4/3 * 4.14 = 5.52 kg.


that's your solution.


to confirm, do the following.


start with 5.52 kg.
take out 1/4 * 5.52 kg to get 4.14 kg left.
take out 2/3 * 4.14 kg to get 1.38 kg left.
add 4.14 kg to that to get 5.52 kg.


the solution is confirmed to be good.
the original amount of peanuts was 5.52 kg.