Allison has 5 time as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?

b=baseball cards

f=football cards

b=5f she has 5 times as many baseball cards as football cards so we multiply the football cards by 5 to make them equal

b+f=120 there are 120 football and baseball cards total

5f+f = 120 substitute 5f everywhere you see a b

6f = 120 combine like terms

f=20 divide by 6

there are 20 football cards

b=5f

b=5 (20)

there are 100 baseball cards

100

let the number of football cards be x then she has 5x baseball cards

the total cards she has is 120, hence

x + 5x = 120

6x = 120 (divide both sides by 6)

x = 20

Allison has 20 football cards and 5 * 20 = 100 baseball cards