Question

ann has some cards beth has 4 more cards than ann catch has 3 times as many cards as beth the total number of cards is 51 how many cards does each of the 3 people have

Answer 1

9514 1404 393

Answer:

• Ann 7
• Beth 11
• Catch 33

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.