Question

Alan has 80% more stamps than Billy. Billy has 3/5 of the number of Charlies stamps. If Billy gave 150 stamps to Charlie, then Charlie would now have three times the number of Billys remaining stamps. What is the total number of stamps they have altogether?

Answer 1

a=alan
b=billy
c=charlie

a is 80% more than charlie means that a is 100% and billy=20%, so 20% of alan=billy
0.2a=c

b has 3/5 of c
b=3/5c

if b-150 and c+150, (c+150)=3 times (b-150)
luckily we can related c and b
b=3/5c
c+150=3(3/5c-150)
distribute
c+150=9/5c-450
add 450 both sides
c+600=9/5c
minus c both sides
600=4/5c
times 5/4 both sides
750=c

charlie has 750 stamps
billy=3/5 times c
b=3/5 times 750
b=450
allan has 80% more than billy
0.2a=b
0.2a=450
divide both sides by 0.2
a=2250

b=450
a=2250
c=750
add them
a+b+c=2250+450+750=3450 stamps

Answer 2

a=alan

b=billy

c=charlie

a is 80% more than charlie means that a is 100% and billy=20%, so 20% of alan=billy

0.2a=c

b has 3/5 of c

b=3/5c

if b-150 and c+150, (c+150)=3 times (b-150)

luckily we can related c and b

b=3/5c

c+150=3(3/5c-150)

distribute

c+150=9/5c-450

add 450 both sides

c+600=9/5c

minus c both sides

600=4/5c

times 5/4 both sides

750=c

charlie has 750 stamps

billy=3/5 times c

b=3/5 times 750

b=450

allan has 80% more than billy

0.2a=b

0.2a=450

divide both sides by 0.2

a=2250

b=450

a=2250

c=750

add them

a+b+c=2250+450+750=3450 stamps