Question

. Tommy gives baseball cards to four of his friends. He gives Kiana 3 cards less than he gives Gary.
He gives Monty 7 cards more than he gives Kiana. He gives Willa twice as many as he gives
Monty. How many cards does Tommy give to each friend if he gives out a total of 74 cards?

Answer 1

Let's call these friends by their first initial:
K = Kiana, G = Gary, M = Monty, W = Willa

Now we can convert the question to a system of linear equations:
Gary has 3 cards more than Kiana, so G = K + 3
Monty has 7 cards more than Kiana, so M = K + 7
Willa has twice as many cards as Monty, so W = 2M = 2(K + 7) = 2K + 14

74 cards given out = all the friends combined, so
74
= K + G + M + W
= K + (K + 3) + (K + 7) + (2K + 14)
= 5K + 3 + 7 + 14
= 5K + 24

50 = 5K
10 = K, so Kiana had 10 cards
G = K + 3 = 13, so Gary had 13 cards
M = K + 7 = 17, so Monty had 17 cards
W = 2M = 34, so Willa had 34 cards

Checking our work, 10 + 13 + 17 + 34 = 74 cards total.