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 ?
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