Algebra question

Question

Gina has $2 more than three times the amount that Fred has. When Gina gave Fred $5, Fred then had one-half as much as Gina. How much do Gina have at first?

Answer 1

Let x = the amount  Fred had

Gina had (3x + 2) based on the info given

 

When Gina gives Fred $5, he now has (x + 5)

At the same time, Gina now has $5 less, so she now has (3x + 2) - 5 = 3x - 3

 

Since Fred now has 1/2 of what Gina has, we can express this as:

 

x + 5 = (1/2) * (3x - 3)

 

Multiply thru by 2 to clear fractions

 

2(x + 5) = 3x - 3

2x + 10 = 3x - 3

2x + 13 = 3x

x = 13

 

So Fred had $13 at first, and Gina had 3x + 2 = 3(13) + 2 = 39 + 2 = $41