Math question please HELP. answer and explanations w/ work please?

Question

beckyhas as many dimes as ryan and amy have together. ryan has 2 more dimes than amy, and amy has one third as many dimes as becky has. how many dimes does each have?

please show all wwork

Answer 1

Let b = Becky, r = Ryan and a = Amy

The three equations are then:

b = r + a   Becky has as many dimes as Ryan and Amy

r = a + 2   Ryan has 2 more dimes than Amy

a = 1/3(b)  Amy has 1/3 as many dimes as Beack

Starting with r = a + 2 substitute a = 1/3(b) for a

r = 1/3(b) + 2

Now substitute the new r equation and the a equation into the first equation:

b = (1/3(b) + 2) + 1/3(b)

b = 1/3(b) + 2 + 1/3(b)

b = 2/3(b) + 2

b - 2/3(b) = 2/3(b) - 2/3(b) + 2

1/3(b) = 2

1/3(b) * 3 = 2 * 3

b = 6

Now plug 6 into the third equation:

a = 1/3(b)

a = 1/3(6)

a = 2

Plug a into the second equation:

r = a + 2

r = 2 + 2

r = 4

Therefore,

Becky has 6 dimes

Ryan has 4 dimes

Amy has 2 dimes

Hope that helps!