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Richard has 4 times as many marbles as John.If Richard gave 18 to John they would have the same number .How many marbles has each

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2 Answers

Let:
   r = current number of Richard's marbles
   j = current number of John's marbles
 
Translate:
"Richard has 4 times as many marbles as John""   means
      r       =   4    *    j            [eq1]
 
"If Richard gave 18 to John they would have the same number"     means
       r         -     18  =   j  +  18           [eq2]
 
 
"How many marbles has each?"   means find  r and j
 
The math:
      r = j + 36         [from eq2]
      4j = j + 36        [substitute that into eq1]
      3j = 36             [subtract j from both side]
       j = 12              [divide both sides by 3]
 
       r = 4(12)         [put value of j into either equation]
      r = 48
 
Check:
   Is   48 = 4*12   ? yes
 
   Is    48-18 = 12 + 18   ?
           30 = 30   ?yes
First, define our variables:
r = # of Richard's marbles
j = # of Johns's marbles
 
"Richard has 4 times as much marbles as John" gives us:
r = 4j
 
"If Richard gave 18 marbles to John they would have the same number" gives us:
r = 18 + j
 
Since both expressions with a j are equal to r, the are equal to each other and solve for j:
4j = 18 + j     subtract j from both sides
3j = 18     divide both sides by 3
j = 6
 
Now find r:
r = 4j = 4(6) = 24
 
So, Richard has 24 marbles and John has 6 marbles.
 
Check:
4(6) = 24 = 18 + 6