Question 1118351: Hi
Half of johns pocket money is 3/7 of toms pocket money. If tom has $2 more than john, how much does john have.
thanks Found 2 solutions by htmentor, greenestamps:Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! Let J = John's money and T = Tom's money
J/2 = (3/7)T [half of John's equals 3/7 of Tom's]
T = J + 2 [Tom has 2 more than John]
Substitute the 2nd equation in the 1st:
J/2 = (3/7)(J + 2)
Solve for J:
J - (6/7)J = 12/7
J = 12
John has 12 dollars, Tom has 14
If a solution using algebra is not required, you can get some good mental exercise solving the problem informally with logical analysis.
If half of John's pocket money is 3/7 of Tom's, then all of John's pocket money is 6/7 of Tom's.
Then if Tom has $2 more than John, you are looking for a fraction that is equivalent to 6/7 in which the denominator is 2 more than the numerator. Since in the fraction 6/7 the denominator is 1 more than the numerator, simply double the numerator and denominator of the fraction: 6/7 = (6*2)/(7*2) = 12/14.
