SOLUTION: Vincent had some peanuts. He ate 1/4 of it last week and 2/3 of the remaining peanuts last night. His mother gave him another 4.14 kg of peanuts just now. Vincent then found th

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Question 1184048: Vincent had some peanuts. He ate 1/4 of it last week and 2/3 of the remaining peanuts
last night. His mother gave him another 4.14 kg of peanuts just now. Vincent then
found that he had as much peanuts as he had at first. How many kilograms of
peanuts did Vincent have at first?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.