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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

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

### 2 Answers by Expert Tutors

David W. | Experienced ProfExperienced Prof
4.4 4.4 (47 lesson ratings) (47)
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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
Kathy M. | ANY MATH -I can break it down to the basics for you!ANY MATH -I can break it down to the bas...
5.0 5.0 (11 lesson ratings) (11)
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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