**j = 12**[divide both sides by 3]

**r = 48**

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 ?

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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]

r = 4(12) [put value of j into either equation]

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

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