9514 1404 393
Answer:
Step-by-step explanation:
Let 'a', 'b', 'c' represent the numbers of cards held by Ann, Beth, and Catch.
b = a +4 . . . . . . Beth has 4 more cards than Ann
c = 3b . . . . . . . . Catch has 3 times as many as Beth
a +b +c = 51 . . . . the total number of cards is 51
Substituting for c, we have ...
a +b +3b = 51
a +4b = 51
Substituting for 'b' we have ...
a +4(a +4) = 51
5a +16 = 51 . . . . . . collect terms
5a = 35 . . . . . . . subtract 16
a = 7 . . . . . . . . divide by 5
b = a +4 = 7 +4 = 11
c = 3b = 3(11) = 33
Ann has 7 cards; Beth has 11 cards; Catch has 33 cards.
