Answer:
Josh had $18 and Carly had $8.
Step-by-step explanation:
Given:
Josh had $10 more than Carly.
Josh gave Carly half of his money, then Carly had more money than josh, so she gave Josh $4. Then they both had $13.
Question asked:
How much money did each person start?
Solution:
Let Carly start with money be [tex]x[/tex]
Then, Josh start with = [tex]x+10[/tex]
According to question:
For Josh : [tex]x+10[/tex]
[tex]x+10-\frac{1}{2} (x+10)+4=13\\\\ x+10-\frac{x}{2}-5 +4=13\\ \\ x-\frac{x}{2}+9=13\\\\ \frac{2x-x}{2} +9=13\\\\ \frac{x}{2} +9=13[/tex]
Subtracting both sides by 9,
[tex]\frac{x}{2} =4\\[/tex]
Multiplying both sides by 2,
[tex]x=8[/tex]
Carly start with money be [tex]x[/tex] = $8
Josh start with = [tex]x+10[/tex] = 8 + 10 = $18
Therefore, at starting, Josh had $18 and Carly had $8.
