Peter had 3/4 as much money as John who had $800. Some money was given to each of them. As a result Peter had 2/3 as much as John. If the amount given to John was twice the amount given to Peter, how much was given to John?
Peter had 3/4 as much money as John who had $800. Some money was given to each of them. As a result Peter had 2/3 as much as John. If the amount given to John was twice the amount given to Peter, how much was given to John?
John had $800
Peter had 3/4 X $800=$600
J+800 and P+600
2/3(J+800)=P+600
J=2P
Solve the following system:
{(2 (J+800))/3 = P+600 | (equation 1)
J = 2 P | (equation 2)
Express the system in standard form:
{(2 J)/3-P = 200/3 | (equation 1)
J-2 P = 0 | (equation 2)
Swap equation 1 with equation 2:
{J-2 P = 0 | (equation 1)
(2 J)/3-P = 200/3 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{J-2 P = 0 | (equation 1)
0 J+P/3 = 200/3 | (equation 2)
Multiply equation 2 by 3:
{J-2 P = 0 | (equation 1)
0 J+P = 200 | (equation 2)
Add 2 × (equation 2) to equation 1:
{J+0 P = 400 | (equation 1)
0 J+P = 200 | (equation 2)
Collect results:
Answer: | JOHN = 400 PETER=200
