Asked by Anonymous
Alice had twice as much money as Peter. After Alice spent 1/6 of her money
and Peter spent
2/3 of his money, they had a total of $720 left.
(a) How much money did Alice and Peter have altogether at first?
(b) Peter spent 3/4 of his remaining money on a bag. What fraction of his
original amount of money did he spend on the bag?
(Give your answer in its simplest form.)
and Peter spent
2/3 of his money, they had a total of $720 left.
(a) How much money did Alice and Peter have altogether at first?
(b) Peter spent 3/4 of his remaining money on a bag. What fraction of his
original amount of money did he spend on the bag?
(Give your answer in its simplest form.)
Answers
Answered by
Anonymous
I will solve part (a) only.
Let x be the amount Peter had at first, in dollars.
Then Alice had 2x dollars.
Write equation for the total remaining money after spending, as you read the problem
(5/6)(2x) + (1/3)x = 720 dollars.
To solve, multiply both sides of the equation by 6 and simplify
10x + 2x = 6*720
12x = 6*720
x = (6*720)/12 = 6*60 = 360.
Peter had $360 at first; Alice had twice of it, i.e. $720 dollars.
Altogether, they had 360 + 720 = 1080 dollars, at first.
Let x be the amount Peter had at first, in dollars.
Then Alice had 2x dollars.
Write equation for the total remaining money after spending, as you read the problem
(5/6)(2x) + (1/3)x = 720 dollars.
To solve, multiply both sides of the equation by 6 and simplify
10x + 2x = 6*720
12x = 6*720
x = (6*720)/12 = 6*60 = 360.
Peter had $360 at first; Alice had twice of it, i.e. $720 dollars.
Altogether, they had 360 + 720 = 1080 dollars, at first.
Answered by
Anonymous
(a)
Let the money Peter had be y, therefore, Alice had 2y.
Total money= (y+2y)=3y
Alice spent (1/6 of 2y)=1/3y
Peter spent (2/3 of y)=2/3y
Total money spent= (1/3y+2/3y)=y
Total money left= (3y-y)=2y
2y=$720 (divide both sides by 2)
y=$360
Peter had $360
Alice had (2×360)=$ 720
Hence, total money is (360+720) =$1080
(b)
After Peter spent 2/3, the remaining fraction of money is (1-2/3)=1/3
(1/3 of $360) =$120
Money spent on the bag =(3/4 of $120)=$90
Therefore, fraction of the amount spent on bag over the original amount
=90/360
=1/4
Let the money Peter had be y, therefore, Alice had 2y.
Total money= (y+2y)=3y
Alice spent (1/6 of 2y)=1/3y
Peter spent (2/3 of y)=2/3y
Total money spent= (1/3y+2/3y)=y
Total money left= (3y-y)=2y
2y=$720 (divide both sides by 2)
y=$360
Peter had $360
Alice had (2×360)=$ 720
Hence, total money is (360+720) =$1080
(b)
After Peter spent 2/3, the remaining fraction of money is (1-2/3)=1/3
(1/3 of $360) =$120
Money spent on the bag =(3/4 of $120)=$90
Therefore, fraction of the amount spent on bag over the original amount
=90/360
=1/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.