Share $1500 among james, peter and mary so that each of the two boys receives twice as much as mary. Calculate the amount of money mary received.
Express Mary's share as a fraction of the total amount.
Express Peters share as a fraction of the amount received by james and mary.
the shares are 2:2:1, so there are 5 parts in total
boys get 2/5 each
Mary gets 1/5
be careful on the last part
Well, since each of the two boys receives twice as much as Mary, we can say that Mary's share is x. Therefore, James and Peter's shares would be 2x and 2x, respectively.
To find the value of x, we can set up the following equation:
x + 2x + 2x = $1500
Simplifying this equation, we get:
5x = $1500
Dividing both sides by 5 gives us:
x = $300
So, Mary received $300.
Now, let's express Mary's share as a fraction of the total amount:
Mary's share = $300
Total amount = $1500
Mary's share as a fraction of total = Mary's share / Total amount
= $300 / $1500
= 1/5
Therefore, Mary's share is 1/5 of the total amount.
Lastly, let's express Peter's share as a fraction of James and Mary's share:
Peter's share = 2 * Mary's share = 2 * $300 = $600
James' share = 2 * Mary's share = 2 * $300 = $600
Peter's share as a fraction of James and Mary's share = Peter's share / (James' share + Mary's share)
= $600 / ($600 + $300)
= $600 / $900
= 2/3
So, Peter's share is 2/3 of the amount received by James and Mary.
Let's solve this step-by-step:
Step 1: Determine the ratio between Mary's share and the boys' shares.
Since each boy receives twice as much as Mary, the ratio is 1:2.
Step 2: Calculate the total of the ratio parts.
The total of the ratio parts is 1+2=3.
So, 1 part represents (1500/3)= $500.
Step 3: Calculate Mary's share.
Since Mary's share is 1 part, she will receive 1 * $500 = $500.
Step 4: Calculate Mary's share as a fraction of the total amount.
Mary's share is $500. The total amount is $1500. So, Mary's share as a fraction is 500/1500 = 1/3.
Step 5: Calculate Peter's share.
Since Peter receives twice as much as Mary, he will receive 2 * $500 = $1000.
Step 6: Calculate Peter's share as a fraction of the amount received by James and Mary.
Peter's share is $1000. James and Mary's total amount is $500 + $500 = $1000. So, Peter's share as a fraction is 1000/1000 = 1.
In conclusion:
Mary received $500.
Mary's share as a fraction of the total amount is 1/3.
Peter's share as a fraction of the amount received by James and Mary is 1.
To solve this problem, we need to follow a step-by-step approach.
Step 1: Let's assign variables to represent the amounts of money received by each person.
Let's call Mary's share "m," James' share "j," and Peter's share "p."
Step 2: Translate the given information into equations.
We know that each of the two boys (James and Peter) receives twice as much as Mary. This can be expressed as:
j = 2m (Equation 1)
p = 2m (Equation 2)
We also know that the total amount shared is $1500, so:
m + j + p = $1500 (Equation 3)
Step 3: Substitute the values from Equation 2 into Equation 3 to solve for m.
m + 2m + 2m = $1500
5m = $1500
m = $1500 / 5
m = $300
So, Mary received $300.
To express Mary's share as a fraction of the total amount, we divide her share by the total amount:
Fraction for Mary = m / (m + j + p)
= $300 / $1500
= 1/5
Therefore, Mary's share is 1/5 of the total amount.
To express Peter's share as a fraction of the amount received by James and Mary, we divide Peter's share by the sum of James and Mary's shares:
Fraction for Peter = p / (j + m)
= ($300 * 2) / ($300 + $600)
= $600 / $900
= 2/3
Therefore, Peter's share is 2/3 of the amount received by James and Mary.