Middle School Math: HELP

Question

The ratio of the number of Yolanda's fish to Zachary's fish is 2:7. Zachary gives Yolanda some fish, and after he does, he has twice as many fish as Yolanda. Yolanda now has 24 fish. How many fish did Zachary give her?

Answer 1

I shall work this problem backwards.

 

At the end

Yolanda has 24 fish

Zachary has 48 fish

 

Before some away are exchanged

Yolanda has 24 - x

Zachary has 48 + x

 

The ratio Yolanda's fish to Zachary's fish is 2 /7

 

(24 - x) / (48 + x) = 2 / 7

96 + 2x = 168 - 7x

96 + 9x = 168

9x = 72

x = 8

 

Zachary gave 8 fish to Yolanda.

Answer 2

This problem has to be solved as a system of equations.

Let x = Zachary's initial fish

Let y = # of fish Zachary gave Yolanda

 

Then

(2/7) x + y = 24 (Yolanda's fish after she got y from Zachary)

and

x - y = 48 (Zachary's fish after he gave away y of them. Twice as many as Yolanda)

 

Solving the system by adding the 2 equations and eliminating y:

 

(2/7) x+ x = 72

(9/7) x = 72

x = 56

 

Now, substitute 56 in for x in one of the equations:

x - y = 48

56 - y = 48

y = 8

Zachary gave 8 fish to Yolanda