Leo and Isaac had 95 marbles altogether. Leo gave away 3 more marbles than Isaac. Isaac was left with 5 fewer than the marbles he gave away. Leo had 2 more marbles left than Isaac. How many marbles did Leo give away?
Draw a model by using the information in the question.
+128474 Let Leo start with N marbles
Then Issac started with 95 - N marbles
Let the number of marbles that Issac gave away = G
Then Leo gave away G + 3
From Issac's point of view
(95 - N) - G = G - 5
95 - N = 2G- 5
95 + 5 - 2G = N
100 - 2G = N (1)
From Leo's point of view
N - (G + 3) = (G - 5) + 2
N - G - 3 = G - 3
N = 2G (2)
Equating (1) and (2) we have
100 - 2G = 2G
100 = 4G
100 / 4 = G = 25
So Leo gane away G + 3 = 28 marbles
Proof
N = 2G = 50 = what Leo started with
95 - 50 = 45 = what Isaac started with
Leo gave away 28 and was left with 22
Isaac gave away 25 and was left with 20
And Leo was left with two more marbles than Isaac
